SATHEE: Thermodynamics - Result Question 29

Thermodynamics - Result Question 29

30. If the ratio of specific heat of a gas at constant pressure to that at constant volume is $γ$ , the change in internal energy of a mass of gas, when the volume changes from $V$ to $2 V$ at constant pressure $P$ , is

[1998]

(a) $\frac{R}{(γ - 1)}$

(b) $P V$

(d) $\frac{γ P V}{(γ - 1)}$

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Answer:

Correct Answer: 30. (c)

Solution:

$Δ W = - Δ U$ (Expansion in the system)

$= - \frac{1}{γ - 1} (P_{1} V_{1} - P_{2} V_{2})$

$Δ U = \frac{1}{1 - γ} (P_{2} V_{2} - P_{1} V_{1})$

Here, $V_{1} = V, V_{2} = 2 V$

$∴ Δ U = \frac{1}{1 - γ} [P \times 2 V - P V] = \frac{P V}{1 - γ}$

$\Rightarrow Δ U = - \frac{P V}{γ - 1}$

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Thermodynamics - Result Question 29

30. If the ratio of specific heat of a gas at constant pressure to that at constant volume is γ, the change in internal energy of a mass of gas, when the volume changes from V to 2V at constant pressure P, is

Answer:

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30. If the ratio of specific heat of a gas at constant pressure to that at constant volume is $γ$ , the change in internal energy of a mass of gas, when the volume changes from $V$ to $2 V$ at constant pressure $P$ , is