Tag: heat and thermodynamics

Questions Related to heat and thermodynamics

Assertion : $C _P$ is always greater than $C _V$ in gases.
Reason : Work done at constant pressure is more than at constant volume.

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

  1. If both assertion and reason are true and reason is the correct explanation of assertion

  2. If both assertion and reason are true but reason is not the correct explanation of assertion

  3. If assertion is true but reason is false

  4. If both assertion and reason are false

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Correct Option: A

$C _{P}$ and $C _{V}$ are specific heats at constant pressure and constant volume, respectively. It is observed that $C _{P} - C _{V} = a$ for hydrogen gas $C _{P} - C _{V} = b$ for nitrogen gas. The correct relation between $a$ and $b$ is

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

  1. $a = b$

  2. $a = 14b$

  3. $a = 28b$

  4. $a = \dfrac {1}{14}b$

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Correct Option: B

If $C _{p} and C _{v}$ denoto the specific heats of nitron per unit mass at constant pressure and constant volume rest then 

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

  1. $C _{p} and C _{v}$=R/28

  2. $C _{p} and C _{v}$=R/14

  3. $C _{p} and C _{v}$=R

  4. $C _{p} and C _{v}$=28R

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Correct Option: A
Explanation:

According to Mayer's relation $C _{p}-C _{v}= R/m$

$C _{p}-C _{v}=\dfrac{R}{m}$
for nitrogen $m=28$
$ \therefore C _{p}- C _{v^{2}} R/28$

$C _v,$ respectively, If $\gamma =\dfrac { { C } _{ p } }{ { C } _{ v } } $ and $R$ is the universal gas constant, then $C _v$ is equal to 

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

  1. $\gamma ^R$

  2. $\dfrac{1+\gamma }{1-\gamma}$

  3. $\dfrac{R}{(\gamma-1)}$

  4. $\dfrac{(\gamma-1)}{R}$

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Correct Option: B

Each molecule of gas has f degree of freedom. The ratio $\dfrac { { C } _{ P } }{ { C } _{ V } } =\gamma $for the gas is 

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

  1. $1+\dfrac { f }{ 2 } $

  2. $1+\dfrac { 1 }{ f } $

  3. $1+\dfrac { 2 }{ f } $

  4. $\dfrac { f }{ 2 } $

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Correct Option: A

The molar specific heat at constant  pressure of an ideal gas is ( 7/2) R. the ratio of specific heat at constant pressure to that at constant volume is 

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

  1. 9/7

  2. 7/5

  3. 8/7

  4. 5/7

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Correct Option: A

Ration of $C _p$ and $C _v$ depends upon temperatures according to the following relation

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

  1. $\gamma \propto T$

  2. $\displaystyle \gamma \propto \frac{1}{T}$

  3. $\gamma \propto \sqrt{T}$

  4. $\gamma \propto T^o$

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Correct Option: D
Explanation:

$\gamma =\dfrac{C _p}{C _v}$ i.e, ratio of specific heat capacity at constant pressure and specific heat capacity at constant volume. It doesn't depend on temperature, i.e, it is independent of temperature.

Which type of ideal gas will have the largest value for $C _p-C _v?$

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

  1. Monoatomic

  2. Diatomic

  3. Polyatomic

  4. The value will be the same for all

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Correct Option: D

For an ideal gas

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

  1. $C _p$ is less than $C _v$

  2. $C _p$ is equal to $C _v$

  3. $C _p$ is greater than $C _v$

  4. $C _p=C _v=0$

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Correct Option: C
Explanation:

 For an ideal gas, $C _p$ is greater than $C _v$ because when gas is heated at constant volume, whole of the heat supplied is used to increase the temperature only but when gas is heated at constant pressure, the heat supplied is used to increases both temperature and the volume of gas (heat is used to do work)

The correct option is C.

Adiabatic exponent of a gas is equal to 

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

  1. $C _p\times C _v$

  2. $\dfrac{C _p}{C _v}$

  3. $C _p-C _v$

  4. $C _p+C _v$

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Correct Option: B