Tag: principal and molar specific heats of gases

Questions Related to principal and molar specific heats of gases

Molar heat capacity of an ideal gas whose molar heat capacity at constant is $C _v$ for process $P=2e^{2v}$( where P is pressure of gas and V is volume of gas)

principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

  1. $C _v + \dfrac{R}{1+2V}$

  2. $C _v + \dfrac{R}{2V}$

  3. $C _v + \dfrac{R}{V}$

  4. None of these

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Correct Option: A
Explanation:

$\begin{array}{l} By\, u\sin  g\, \, first\, law\, of\, Ther{ { moodynamics } }:- \ dQ=dw+dU \ and,\, also\,  \ dQ=nCdT \ dw=Pdv \ dU=n{ C _{ v } }dT \ Now,\, substituting\, them\, in\, the\, first\, law\, we\, get \ \Rightarrow nCdT=PdV+n{ C _{ n } }dT \ C=\frac { { PdV } }{ { ndT } } +{ C _{ v } } \ To\, find\, \, \frac { { PdV } }{ { ndT } } \, we\, will\, use\, the\, ideal\, gas\, equation \ PV=nRT \ 2V{ e^{ 2V } }=nRT\, \, \, \, \, \, \left[ { \, { { Re } }place\, \, P=2{ e^{ 2v } } } \right]  \ Differentiating\, both\, sides\, with\, respect\, to\, T \ 2\left( { { e^{ 2V } }+2V{ e^{ 2V } } } \right) \frac { { dV } }{ { dT } } =nR \ Now,\, from\, this\, we\, have \ \frac { { PdV } }{ { ndT } } =\frac { R }{ { 1+2v } }  \ So,\, we\, get \ C={ C _{ v } }+\frac { R }{ { 1+2v } }  \ Hence,\, the\, option\, A\, is\, the\, correct\, answer. \end{array}$

For a certain gas the heat capacity at constant pressure is greater than that at constant volume by $29.1 J/K$. How many moles of the gas are there?

principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

  1. $13.5 \ mol $

  2. $9.5 \ mol $

  3. $7.5 \ mol $

  4. $3.5 \ mol $

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Correct Option: D
Explanation:

We know that for one mole of gas,


${ C } _{ P }-{ C } _{ V }=8.32J/K$

Hence, for n moles,

$n({ C } _{ P }-{ C } _{ V })=8.32n=29.1$

$n=3.5 mol$

Answer is $3.5 mol$

4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 ${ JK }^{ -1 }{ mol }^{ -1 }$. If the speed of sound in this gas at NTP is 952${ ms }^{ -1 }$, then the heat capacity at constant pressure is (Take gas constant R=8.3${ JK }^{ -1 }{ mol }^{ -1 }$)

principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

  1. $8.5{ JK }^{ -1 }{ mol }^{ -1 }$

  2. $8.0{ JK }^{ -1 }{ mol }^{ -1 }$

  3. $7.5{ JK }^{ -1 }{ mol }^{ -1 }$

  4. $7.0{ JK }^{ -1 }{ mol }^{ -1 }$

Show answer
Correct Option: B

When an ideal diatomic gas is heated at a constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is

principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

  1. $\dfrac {2}{5}$

  2. $\dfrac {3}{5}$

  3. $\dfrac {3}{7}$

  4. $\dfrac {5}{7}$

Show answer
Correct Option: D
Explanation:

$Th\quad fraction\quad is\quad \frac { \triangle V }{ \triangle Q } \quad =\quad \frac { { _{ n }{ C } _{ v } }\triangle T }{ { _{ n }{ C } _{ p } }\triangle T } \ \frac { \triangle V }{ \triangle Q } =\frac { { C } _{ V } }{ { C } _{ P } } \quad =\quad \frac { 1 }{ Y } \ as\quad we\quad know\quad y\quad =\quad { C } _{ P }/{ C } _{ V }\ y\quad for\quad diatomatic\quad gas\quad :\quad \ { C } _{ P }\quad of\quad diatometic\quad gas\quad :\quad \frac { 7 }{ 2 } \ { C } _{ V }\quad of\quad diatometic\quad gas\quad :\quad \frac { 5 }{ 2 } \ y\quad =\quad \frac { { C } _{ P } }{ { C } _{ V } } =\frac { 7/2 }{ 5/2 } =\frac { 7 }{ 5 } \ \frac { \triangle V }{ \triangle Q } =\frac { 1 }{ y } =\frac { 1 }{ 7/5 } =\frac { 5 }{ 7 } \quad (D)$

For an ideal gas, the heat capacity at constant pressure is larger than that at constant volume because

principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

  1. positive work is done during expansion of the gas by the external pressure

  2. positive work is done during expansion by the gas against external pressure

  3. positive work is done during expansion by the gas against intermolecular forces of attraction

  4. more collisions occur per unit time when volume is kept constant

Show answer
Correct Option: B
Explanation:

When  heat  is  supplied  at  constant  volume,  temperature  increases accordingly  to  the  ideal  gas  equation.

$P=\dfrac { nRT }{ V } $

as  V  is  constant  and  T  is  increasing,  pressure  will  also  increase.

Than at constant pressure  as temperature is increase volume increases, resulting in expansion of the gas, resulting in positive work, Hence the heat given is used up for expansion and then to increases the internal energy . The heat capacity at constant pressure is larger.