Tag: heat and thermodynamics

Quizzes (20) Questions (162)

Questions Related to heat and thermodynamics

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

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

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Cp is greater than Cv because at constant pressure, the system does work on the surroundings as it expands, requiring additional heat input to achieve the same temperature rise. The reason correctly explains the assertion.

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

$C _{P}$ 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

  1. $a = b$
  2. $a = 14b$
  3. $a = 28b$
  4. $a = \dfrac {1}{14}b$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For any ideal gas, Cp - Cv = R (in molar terms). If 'a' and 'b' refer to specific heats (per unit mass), then Cp - Cv = R/M, where M is molar mass. For hydrogen, M=2; for nitrogen, M=28. Thus, a = R/2 and b = R/28. Therefore, a/b = 28/2 = 14, so a = 14b.

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

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

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
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$

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

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

  1. $\gamma ^R$
  2. $\dfrac{1+\gamma }{1-\gamma}$
  3. $\dfrac{R}{(\gamma-1)}$
  4. $\dfrac{(\gamma-1)}{R}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From Mayer's relation Cp - Cv = R and the definition of adiabatic index gamma = Cp / Cv, we can substitute Cp = gamma * Cv into Mayer's relation to get Cv(gamma - 1) = R, which rearranges to Cv = R / (gamma - 1).

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

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

  1. $1+\dfrac { f }{ 2 } $
  2. $1+\dfrac { 1 }{ f } $
  3. $1+\dfrac { 2 }{ f } $
  4. $\dfrac { f }{ 2 } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the equipartition theorem, internal energy U = (f/2)RT, so Cv = dU/dT = (f/2)R. Then Cp = Cv + R = ((f/2) + 1)R. Taking their ratio gamma = Cp / Cv gives 1 + (2 / f).

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

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 

  1. 9/7

  2. 7/5

  3. 8/7

  4. 5/7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For an ideal gas, the ratio of molar specific heats is given by gamma = Cp / Cv. Using the relation Cp - Cv = R, we find Cv = Cp - R = (7/2)R - R = (5/2)R. Therefore, gamma = (7/2)R / ((5/2)R) = 7/5.

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

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

  1. $\gamma \propto T$
  2. $\displaystyle \gamma \propto \frac{1}{T}$
  3. $\gamma \propto \sqrt{T}$
  4. $\gamma \propto T^o$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  1. Monoatomic

  2. Diatomic

  3. Polyatomic

  4. The value will be the same for all
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For all ideal gases, the difference between molar heat capacity at constant pressure and constant volume is defined by the universal gas constant, Cp - Cv = R. This value is independent of the atomicity of the gas.

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

For an ideal gas

  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. $C _p=C _v=0$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.