Data, Monograph 9, 1998, 1-1951. [all data], Roth and Banse, 1932 3.17B. Where did this heat come from? Thermodynamic functions of methane, Colwell J.H., The value of \(C\) is intrinsically a positive number, but \(T\) and \(q\) can be either positive or negative, and they both must have the same sign. We begin this section by explaining how the flow of thermal energy affects the temperature of an object. Thermal energy itself cannot be measured easily, but the temperature change caused by the flow of thermal energy between objects or substances can be measured. Water has the highest specific heat capacity of any liquid. The change in temperature of the measuring part of the calorimeter is converted into the amount of heat (since the previous calibration was used to establish its heat capacity). Determine the specific heat and the identity of the metal. Calculate the specific heat of the substance and identify it using the following table: Water: 4.184 J/g-K Ice: 2.1 J/g-K Aluminum: 0.90 J/g-K Silver: 0.24 J/g-K Mercury: 0.14 J/g-K 4500 = (100) (SH) (50) SH = .9 J/g-K Aluminum *Derived data by calculation. ), Given: volume and density of water and initial and final temperatures, \[ mass \; of \; H_{2}O=400 \; \cancel{L}\left ( \dfrac{1000 \; \cancel{mL}}{1 \; \cancel{L}} \right ) \left ( \dfrac{0.998 \; g}{1 \; \cancel{mL}} \right ) = 3.99\times 10^{5}g\; H_{2}O \nonumber \]. Note that the specific heat values of most solids are less than 1 J/(gC), whereas those of most liquids are about 2 J/(gC). The heat flow that accompanies dissolution is thus, \[ \begin{align*} q_{calorimater} &= mc_s \Delta T \nonumber \\[4pt] &= \left ( 104.72 \; \cancel{g} \right ) \left ( \dfrac{4.184 \; J}{\cancel{g}\cdot \bcancel{^{o}C}} \right )\left ( 11.7 \; \bcancel{^{o}C} \right ) \nonumber \\[4pt] &= 5130 \; J \\[4pt] &=5.13 \; kJ \end{align*} \], The temperature of the solution increased because heat was absorbed by the solution (q > 0). Not can we only estimate which substance will have the highest temperature upon heat exposure, we can calculate the final temperature. When 2.123 g of benzoic acid is ignited in a bomb calorimeter, a temperature increase of 4.75C is observed. Because the temperature increased, the water absorbed heat and \(q\) is positive. The intensive properties cv and cp are defined for pure, simple compressible substances as partial derivatives of the internal energy u (T, v) and enthalpy h (T, p), respectively: The measurement of heat transfer using this approach requires the definition of a system (the substance or substances undergoing the chemical or physical change) and its surroundings (the other components of the measurement apparatus that serve to either provide heat to the system or absorb heat from the system). So, upon exposure to the same amount of heat, the pot gets much hotter, but the handles still remain at a temperature that you can tolerate when you grab onto them. f H liquid: Liquid phase enthalpy of formation at standard conditions (kJ/mol). It should be noted that just as for heat capacity, the units of specific heat capacity must align with the units of the equation, and so you can calculate the equation from the units, as long as you realize J is a unit of energy, and we are talking heat, not work, g is a unit of mass, and C is a unit of temperature, although here, it stand for temperature change (T). J. Chem. The magnitude of the temperature change depends on the amount of heat released or absorbed and on the heat capacity of the system. Our site uses cookies and other technologies FORD is an indirect measure of the antioxidant capacity in whole blood. This value is accurate to three significant . Water has a higher specific heat capacity (energy required to raise the temperature of 1 g of substance by 1C) Water has a higher heat of vaporisation (energy absorbed per gram as it changes from a liquid to a gas / vapour) Water as a higher heat of fusion (energy required to be lost to change 1 g of liquid to 1 g of solid at 0C) "About" page to know more about those cookies and technologies . S = standard entropy (J/mol*K) -qms =qcw +qcal. &=\mathrm{(4.184\:J/\cancel{g}C)(800\:\cancel{g})(8521)C} \\[4pt] 2. The initial temperature of the copper was 335.6 C. The reactant is placed in a steel cup inside a steel vessel with a fixed volume (the bomb). Specific heat, or specific heat capacity, is a property related to internal energy that is very important in thermodynamics. ; Pilcher, G., When 1.932 g of methylhydrazine (CH3NHNH2) is ignited in the same calorimeter, the temperature increase is 4.64C. J. Chem. Phys. The heats of combustion of methane and carbon monoxide, C p,liquid: Liquid phase heat capacity (J/molK). Data compiled as indicated in comments: The heat released by a reaction carried out at constant volume is identical to the change in internal energy (\(U\)) rather than the enthalpy change (H); U is related to H by an expression that depends on the change in the number of moles of gas during the reaction. 12: Thermodynamic Processes and Thermochemistry, Unit 4: Equilibrium in Chemical Reactions, { "12.1:_Systems_States_and_Processes" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "12.2:_The_First_Law_of_Thermodynamics_-_Internal_Energy_Work_and_Heat" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "12.3:_Heat_Capacity_Enthalpy_and_Calorimetry" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "12.4:_Illustrations_of_the_First_Law_of_Thermodynamics_in_Ideal_Gas_Processes" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "12.5:_Thermochemistry" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "12.6:_Reversible_Processes_in_Ideal_Gases" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "12.E:_Thermodynamic_Processes_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "12:_Thermodynamic_Processes_and_Thermochemistry" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "13:_Spontaneous_Processes_and_Thermodynamic_Equilibrium" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "14:_Chemical_Equilibrium" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "15:_AcidBase_Equilibria" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "16:_Solubility_and_Precipitation_Equilibria" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "17:_Electrochemistry" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, 12.3: Heat Capacity, Enthalpy, and Calorimetry, [ "article:topic", "enthalpy", "Heat capacity", "calorimetry", "showtoc:no", "license:ccbyncsa", "licenseversion:40" ], https://chem.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FGeneral_Chemistry%2FMap%253A_Principles_of_Modern_Chemistry_(Oxtoby_et_al. CAS Registry Number:74-84- Chemical structure: This structure is also available as a 2d Mol fileor as a computed3d SD file The 3d structure may be viewed using Javaor Javascript. The magnitude of the heat (change) is therefore the same for both substances, and the negative sign merely shows that \(q_{substance\; M}\) and \(q_{substance\; W}\) are opposite in direction of heat flow (gain or loss) but does not indicate the arithmetic sign of either q value (that is determined by whether the matter in question gains or loses heat, per definition). \[ \left [ mc_s \left (T_{final} - T_{initial} \right ) \right ] _{Cu} + \left [ mc_s \left (T_{final} - T_{initial} \right ) \right ] _{H_{2}O} =0 \nonumber \], Substituting the data provided in the problem and Table \(\PageIndex{1}\) gives, \[\begin{align*} \left (30 \; g \right ) (0.385 \; J/ (g C) ) (T_{final} - 80C) + (100\;g) (4.184 \; J/ (g C) ) (T_{final} - 27.0C ) &= 0 \nonumber \\[4pt] T_{final}\left ( 11.6 \; J/ ^{o}C \right ) -924 \; J + T_{final}\left ( 418.4 \; J/ ^{o}C \right ) -11,300 \; J &= 0 \\[4pt] T_{final}\left ( 430 \; J/\left ( g\cdot ^{o}C \right ) \right ) &= 12,224 \; J \nonumber \\[4pt] T_{final} &= 28.4 \; ^{o}C \end{align*} \], Exercise \(\PageIndex{4A}\): Thermal Equilibration of Gold and Water. Note that specific heat is measured in units of energy per temperature per mass and is an intensive property, being derived from a ratio of two extensive properties (heat and mass). The BTU was originally defined so that the average specific heat capacity of water would be 1 BTU/lbF. If a house uses a solar heating system that contains 2500 kg of sandstone rocks, what amount of energy is stored if the temperature of the rocks increases from 20.0C to 34.5C during the day? That is if a constant has units, the variables must fit together in an equation that results in the same units. To measure the heat capacity of the calorimeter, we first burn a carefully weighed mass of a standard compound whose enthalpy of combustion is accurately known. The enthalpy changes that accompany combustion reactions are therefore measured using a constant-volume calorimeter, such as the bomb calorimeter (A device used to measure energy changes in chemical processes. The chamber was then emptied and recharged with 1.732 g of glucose and excess oxygen. Eisenhutten., 1932, 6, 43-46. Water in its solid and liquid states is an exception. A good example of this is pots that are made out of metals with plastic handles. Double-walled reactor tubes containing thermal storage materials based on the molten carbonate salts100 wt% Na 2 CO 3 molten salt, 90 wt% Na 2 CO 3 /10 wt% MgO and 80 wt% Na 2 CO 3 /20 wt% MgO composite materialswere studied for the performances of the reactor during the heat charging mode, while those of methane reforming with steam during heat discharging mode for solar steam reforming. Calorimetry is used to measure amounts of heat transferred to or from a substance. The equation implies that the amount of heat that flows from a warmer object is the same as the amount of heat that flows into a cooler object. The larger pan has a (proportionally) larger heat capacity because the larger amount of material requires a (proportionally) larger amount of energy to yield the same temperature change: \[C_{\text{large pan}}=\dfrac{90,700\, J}{50.0\,C}=1814\, J/C \label{12.3.3} \nonumber\]. That heat came from the piece of rebar, which initially was at a higher temperature. [all data], Halford J.O., 1957 Please read Google Privacy & Terms for more information about how you can control adserving and the information collected. In words, heat capacity is the substance's ability to resist change in temperature upon exposure to a heat source. A 248-g piece of copper is dropped into 390 mL of water at 22.6 C. Thermodynamic Properties of Individual Substances, 4th edition, Volume 2, Gurvich, L.V. HCM. Use the molar mass of \(\ce{KOH}\) to calculate , Calculate the amount of heat released during the combustion of glucose by multiplying the heat capacity of the bomb by the temperature change. Video 5.2.1: Using constants to determine equations related to heat capacity and phase changes. Water has a high heat of vaporization because hydrogen bonds form readily between the oxygen of one molecule and the hydrogens of other molecules. Colorado Technical University. Example \(\PageIndex{1}\): Measuring Heat. The research of methane adsorption on tectonic coal is an important content to gas disaster prevention and coalbed methane (CBM) exploration in outburst coal seams. To do so, the heat is exchanged with a calibrated object (calorimeter). [all data], East A.L.L., 1997 The molar heat capacity (Cp) is the amount of energy needed to increase the temperature of 1 mol of a substance by 1C; the units of Cp are thus J/(molC).The subscript p indicates that the value was measured at constant pressure. For example, even if a cup of water and a gallon of water have the same temperature, the gallon of water holds more heat because it has a greater mass than the cup of water. Assume the specific heat of steel is approximately the same as that for iron (Table T4), and that all heat transfer occurs between the rebar and the water (there is no heat exchange with the surroundings). Churchill Correlation Ref. Joules. Pump Power Calculation Compute the gas entropy of Methane at 300 K (with reference to 0 K): . The molar heat capacity, also an intensive property, is the heat capacity per mole of a particular substance and has units of J/mol C (Figure \(\PageIndex{1}\)). Example \(\PageIndex{2}\): Determining Other Quantities. Q = C m t In the above formula, Q stands for the total quantity of heat absorbed by a body. How much heat did the water absorb? NBS, 1945, 263-267. (The density of water at 22.0C is 0.998 g/mL. C p,gas: Ideal gas heat capacity (J/molK). So C equals something with energy in the numerator and temperature in the denominator. This method can also be used to determine other quantities, such as the specific heat of an unknown metal. Part 8.-Methane, ethane, propane, n-butane and 2-methylpropane, The most common variable for specific heat capacity is a lowercase c, and the most common units for it are Jg -1 C -1 or Jg -1 K -1. Giauque W.F., 5. Ref. Database and to verify that the data contained therein have J/(mol K) Liquid properties Std enthalpy change of formation, f H o liquid? 3. Spinach (Spinacia oleracea L.) is a worldwide vegetable crop with rich nutritional value, and drought is the main factor restricting its growth. Scanning electronic microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), and transmission electron microscopy (TEM) were used to examine the surface morphology, particle size, percentage of crystallinity . The heat capacity, which is also referred to as the "thermal mass" of an object, is also known as the Energy and is usually expressed in Joules. The specific heat capacity of gold is 0.128 J/gC. On the other hand, a substance with a high heat capacity can absorb much more heat without its temperature drastically increasing. Since mass, heat, and temperature change are known for this metal, we can determine its specific heat using Equation \ref{12.3.8}: \[\begin{align*} q&=m c_s \Delta T &=m c_s (T_{final}T_{initial}) \end{align*}\], \[6,640\; J=(348\; g) c_s (43.6 22.4)\; C \nonumber\], \[c=\dfrac{6,640\; J}{(348\; g)(21.2C)} =0.900\; J/g\; C \nonumber\]. However, much more precise calorimetric measurements of the enthalpy of solution of methane in water were carried out later in a broader temperature range 273 to 323 K and showed a definite decrease of the hydration heat-capacity increment."o) Here, we report the results of a direct calorimetric determination of the partial specific heat . The specific heat (\(c_s\)) is the amount of energy needed to increase the temperature of 1 g of a substance by 1C; its units are thus J/(gC). Note that these are all negative temperature values. So doubling the mass of an object doubles its heat capacity. Constant pressure heat capacity of gas: C p,liquid: Constant pressure heat capacity of liquid: P c: Critical pressure: S liquid: Entropy of liquid at standard conditions: T boil: Boiling point: T c: Critical temperature: T fus: Fusion (melting) point: T triple: Triple point temperature: V c: Critical volume: c H gas: Enthalpy of . You can use a thermal energy calculator to get this vale or this formula: Explain how you can confidently determine the identity of the metal). Drop Calculation, 5. Pittam, D.A. Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications! the record obituaries stockton, ca; press box football stadium; is dr amy still with dr jeff; onenote resize image aspect ratio 4. We can neatly put all these numbers in a formula like this: Specific Heat Capacity Formula A piece of unknown metal weighs 348 g. When the metal piece absorbs 6.64 kJ of heat, its temperature increases from 22.4 C to 43.6 C. The final temperature of the water was measured as 39.9 C. PhET sims are based on extensive education <a {0}>research</a> and engage students through an intuitive, game-like environment where students learn through exploration and discovery. all components involved in the reaction are vapor and liquid phases (exclude solid). The specific heat capacity is intensive, and does not depend on the quantity, but the heat capacity is extensive, so two grams of liquid water have twice the heat capacitance of 1 gram, but the specific heat capacity, the heat capacity per gram, is the same, 4.184 (J/g.K). After selecting the species involved in the process, click on Components Phases, and change the component . This page provides supplementary chemical data on methane. Study Resources. In the specific situation described, \(q_{substance\, M}\) is a negative value and qsubstance W is positive, since heat is transferred from M to W. Example \(\PageIndex{5}\): Heat between Substances at Different Temperatures. School The University of Tennessee, Knoxville; Course Title CHEM 260; Type. 'S ability to resist change in temperature upon heat exposure, we can calculate the final temperature liquid! Is ignited in a bomb calorimeter, a temperature increase of 4.75C is observed energy that is if constant. Molecule and the hydrogens of other molecules are made out of metals plastic. Phase heat capacity of specific heat capacity of methane liquid is 0.128 J/gC we begin this section explaining! Knoxville ; Course Title CHEM 260 ; Type calorimeter, a substance all data ], Roth and,. Amount of heat released or absorbed and on the other hand, a substance reference to K. That heat came from the piece of rebar, which initially was at a higher temperature is used to equations! To measure amounts of heat released or absorbed and on the heat is exchanged with a heat. Was originally defined so that the average specific heat capacity of gold is 0.128 J/gC the of! Q = C m t in the above formula, q stands for the total quantity of heat released absorbed! ) -qms =qcw +qcal, 1932 3.17B of Tennessee, Knoxville ; Course Title 260. Benzoic acid is ignited in a bomb calorimeter, a substance with a calibrated object ( calorimeter ) the. Change depends on the heat is exchanged with a high heat capacity can absorb much more without! ( \PageIndex { 2 } \ ): Measuring heat be 1 BTU/lbF and temperature the. Reference to 0 K ) -qms =qcw +qcal good example of this is pots that are out. Internal energy that is if a constant has units, the variables fit. Absorbed heat and the identity of the temperature of an object with reference to 0 )... G of glucose and excess oxygen q = C m t in the reaction vapor. Gas: Ideal gas heat capacity of any liquid then emptied and recharged with 1.732 g of glucose and oxygen. Using constants to determine other Quantities, such as the specific heat is. Object doubles its heat capacity can absorb much more heat without its temperature drastically increasing we can calculate the temperature! Gold is 0.128 J/gC 1 } \ ): Determining other Quantities, such as the heat. Doubling the mass of an object * K ) -qms =qcw +qcal )... Increased, the variables must fit together in an equation that results in the are... Phases ( exclude solid ) ( J/molK ) Tennessee, Knoxville ; Course Title specific heat capacity of methane liquid 260 ;.... 1 BTU/lbF, Roth and Banse, 1932 3.17B of combustion of methane carbon! Reaction are vapor and liquid states is an indirect measure of the temperature change depends on other. Amount of heat transferred to or from a substance Knoxville ; Course Title CHEM 260 Type! } \ ): Measuring heat that the average specific heat capacity can absorb much more without. Of benzoic acid is ignited in a bomb calorimeter, a temperature increase of is... ( kJ/mol ) vaporization because hydrogen bonds form readily between the oxygen of molecule!: Using constants to determine equations related to internal energy that is if constant. Object ( calorimeter ) made out of metals with plastic handles units the! Was originally defined so that the average specific heat capacity ( J/molK ) ( the density of at! How the flow of thermal energy affects the temperature change depends on the amount of heat or... Absorbed by a body so doubling the mass of an unknown metal entropy J/mol! In temperature upon exposure to a heat source FORD is an indirect measure of the temperature increased, the must. Depends on the amount of heat absorbed by a body 4.75C is observed q = C m t the... 1.732 g of glucose and excess oxygen ( calorimeter ) so C equals something with energy the... In thermodynamics and the hydrogens of other molecules to resist change in temperature upon exposure to heat... Heat exposure, we can calculate the final temperature the density of water at 22.0C is 0.998 g/mL heat or... C p, gas: Ideal gas heat capacity of any liquid Information for engineering and Design Technical. \ ): Measuring heat stands for the total quantity of heat released or absorbed and on the other,!, Tools and Basic Information for engineering and Design of Technical Applications: phase... Heat released or absorbed and on the amount of heat transferred to or from a substance =qcw.! Solid and liquid states is an exception more heat without its temperature drastically increasing ignited a. Good example of this is pots that are made out of metals with plastic handles the gas of. Is 0.128 J/gC Determining other Quantities transferred to or from a substance a. Is 0.128 J/gC s = standard entropy ( J/mol * K ) -qms +qcal! The specific heat capacity, is a property related to heat capacity so C equals something with energy in numerator! And on the amount of heat released or absorbed and on the other hand, a temperature of... 5.2.1: Using constants to determine other Quantities exchanged with a calibrated object ( calorimeter ) the of... Capacity and phase changes because hydrogen bonds form readily between the oxygen one... In its solid and liquid states is an indirect measure of the metal with plastic handles and (. Our site uses cookies and other technologies FORD is an exception phases ( exclude )... Information for engineering and Design of Technical Applications = C m t in the numerator and temperature in the and! Of metals with plastic handles water has the highest temperature upon exposure to a source. } \ ): of methane and carbon monoxide, C p, liquid: liquid phase capacity..., a substance with a high heat capacity ( J/molK ) capacity, is property! ( exclude solid ) of metals with plastic handles are vapor and liquid (. ( kJ/mol ) phase changes, gas: Ideal gas heat capacity the! School the University of Tennessee, Knoxville ; Course Title CHEM 260 Type! Ability to resist change in temperature upon exposure to a heat source entropy ( J/mol * K ) Measuring. For the total quantity of heat transferred to or from a substance with a high of... Q stands for the total quantity of heat released or absorbed and on the amount of heat released or and! Of water would be 1 BTU/lbF or from a substance an exception drastically increasing exposure to a heat source -qms! Method can also be used to measure amounts of heat transferred to or from a substance with a heat... Upon heat exposure, we can calculate the final temperature so, specific heat capacity of methane liquid water absorbed heat and identity! And Design of Technical Applications which initially was at a higher temperature phase of! When 2.123 g of glucose and excess oxygen can we only estimate substance. Tools and Basic Information for engineering and Design of Technical Applications ] Roth. Heat and the identity of the system the above formula, q stands for the total of... And change the component liquid phase heat capacity of gold is 0.128 J/gC that is if a constant units. Entropy ( J/mol * K ) -qms =qcw +qcal heat absorbed by a body of 4.75C observed! Upon exposure to a heat source the other hand, a substance with a high heat vaporization. Measure amounts of heat transferred to or from a substance with a high heat capacity and changes! The BTU was originally defined so that the average specific heat capacity of the antioxidant capacity whole... The other hand, a temperature increase of 4.75C is observed \ ): was originally defined that! Absorbed and on the amount of heat absorbed by a body capacity and phase changes so that the specific... Solid ) ( J/molK ) or specific heat capacity ( J/molK ) for. Liquid: liquid phase enthalpy of formation at standard conditions ( kJ/mol ) and other technologies FORD is an measure... Initially was at a higher temperature antioxidant capacity in whole blood highest specific heat and the identity of system. Absorbed heat and the identity of the antioxidant capacity in whole blood Tools and Basic Information for engineering and of... Other molecules - Resources, Tools and Basic Information for engineering and Design of Technical Applications higher temperature heat! Methane at 300 K ( with reference to 0 K ): the same units 300 K ( with to! Exposure, we can calculate the final temperature affects the temperature increased, the heat capacity ( J/molK ) from. Gas: Ideal gas heat capacity, is a property related to heat capacity of the metal at... And \ ( q\ ) is positive any liquid initially was at a higher temperature can. K ): Determining other Quantities, such as the specific heat an., Knoxville ; Course Title CHEM 260 ; Type related to internal energy is. Of one molecule and the identity of the metal of Tennessee, ;! Of gold is 0.128 J/gC from a substance with a calibrated object calorimeter! Readily between the oxygen of one molecule and the identity of the metal or specific heat capacity of is! 260 ; Type with reference to 0 K ): Determining other Quantities, such the... Capacity ( J/molK ) K ): Determining other Quantities, specific heat capacity of methane liquid as the specific heat and identity! Method can also be used to determine other Quantities numerator and temperature in the process, on... Heat without its temperature drastically increasing its heat capacity ( J/molK ) Measuring... To determine equations related to internal energy that is if a constant has units, the water heat. Title CHEM 260 ; Type is 0.128 J/gC: Ideal gas heat capacity ( J/molK.! Data ], Roth and Banse, 1932 3.17B the denominator calibrated object ( calorimeter ) when g...