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Q.

Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K. The piston of A is free to move while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K, then the rise in temperature of the gas in B is

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a

18 K

b

50 K

c

42 K

d

30 K

answer is D.

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Detailed Solution

In both cylinders A and B the gases are diatomic ( $γ$ = 1.4). Piston A is free to move i.e. it is isobaric process. Piston B is fixed i.e. it is isochoric process. If same amount of heat $∆$ Q is given to both then
$∆ Q_{i s o b a r i c} = ∆ Q_{i s o c h o r i c}$

⇒ $μ C_{P} {(∆ T)}_{A} = μ C_{V} {(∆ T)}_{B}$

${(∆ T)}_{B} = \frac{C_{P}}{C_{V}} (∆ T_{A})$ = $γ (∆ T_{A}) = 1.4 \times 30 = 42 K$

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