Thermodynamics - Result Question 18

19. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{C_p}{C_v}$ for the gas is

[2013]

(a) 2

(b) $\frac{5}{3}$

(c) $\frac{3}{2}$

(d) $\frac{4}{3}$

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Answer:

Correct Answer: 19. (c)

Solution:

  1. (c) According to question $P \propto T^{3}$

But as we know for an adiabatic process the

pressure $P \propto T^{\frac{\gamma}{\gamma-1}}$.

So, $\frac{\gamma}{\gamma-1}=3 \Rightarrow \gamma=\frac{3}{2}$ or, $\frac{C_p}{C_v}=\frac{3}{2}$



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