First slide

Heat ;work and internal energy

Question

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:

Moderate

A

18 K
B

30 K
C

42 K
D

50 K

Solution

in first case heat is supplied at constant pressure
$∴ Q_{A} {=nC}_{p} {ΔT}_{1}$
And in second case heat is supplied at constant volume
$∴ Q_{B} {=nC}_{v} {ΔT}_{2}$
here n = number of moles of gas
$C_{P}$ = specific heat of gas at constant pressure
$C_{v}$ =specific heat of gas at constant volume
$∆ T$ =change in temperature
$\begin{array}{rcl} Q_{B} & = & Q_{A} a s a m o u n t o f h e a t g i v e n i s s a m e \\ {nC}_{v} {ΔT}_{2} & = & {nC}_{p} {ΔT}_{1} \end{array}$
For ${ΔT}_{2} = \frac{C_{ρ}}{C_{v}} . {ΔT}_{1}$
substitute specific heat ratio for diatomic gas =7/5
${ΔT}_{2} = \frac{7}{5} .30 = 42 K$ =rise in temperature of gas in B

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