Tag: principal and molar specific heats of gases

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

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)

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

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

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

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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?

  1. $13.5 \ mol $

  2. <span>$9.5 \ mol $</span>

  3. <span>$7.5 \ mol $</span>

  4. <span>$3.5 \ mol $</span>
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $3.5 mol$

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

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${ JK }^{ -1 }{ mol }^{ -1 }$)

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

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

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

  4. $7.0{ JK }^{ -1 }{ mol }^{ -1 }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

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

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

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

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

  4. $\dfrac {5}{7}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

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

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

  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
Reveal answer Fill a bubble to check yourself
B Correct answer
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.