First slide

First law of thermodynamics

Question

A gas is suddenly expanded such that its final volume becomes 3 times its initial volume. If the specific heat at constant volume of the gas is 2R, then the ratio of initial to final pressure is nearly equal to:

Easy

A

5
B

6.5
C

7
D

3.5

Solution

$γ = 1 + \frac{R}{C_{V}} = 1 + \frac{R}{2 R} = 1.5 and P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ} \Rightarrow P_{2} = 3^{1.5} P_{1} \approx 5 P_{1}$

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