First slide

Heat given

Question

Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K. Piston A is free to move and piston of B is fixed. Same amount of heat is given to the gases in the two cylinders. Temperature of the gas in cylinder A increases by 30 K, then increase in temperature of the gas in the cylinder B is ( $γ$ = 14 for diatomic gas) [EAMCET 2013]

Moderate

A

24 K
B

36 K
C

54 K
D

42 K

Solution

We know that, $d Q = n C_{p} d T_{A} = n C_{V} d T_{B}$
$∵$ $n C_{p} d T_{A} = n C_{V} d T_{B}$
$\Rightarrow \frac{C_{p}}{C_{V}} = \frac{d T_{B}}{d T_{A}}$
$\Rightarrow γ = \frac{d T_{B}}{d T_{A}}$ $(∵ γ = \frac{C_{p}}{C_{V}})$
$\Rightarrow d T_{B} = γ d T_{A} = 1.4 \times 30 = 42 K$

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