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Two cylinders...

Question

Two cylinders A and B fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 K$ . The piston of A is free to move while that of B is held fixed Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in A is $42 K$ , the rise in temperature of the gas in B is: $(γ = \frac{5}{3})$

21K

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35K

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42K

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70K

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Solution

The correct option is D 70K
Piston of A is free to move, implies heat is added at constant pressure.
$d Q = n C_{p} d T_{1} = n C_{v} d T_{1} + n R d T_{1}$
Piston B, the heat is added at constant volume
$d Q = d U = n C_{v} d T_{2}$

Given that same amount of heat is supplied.
$∴ n C_{v} d T_{1} + n R d T_{1} = n C_{v} d T_{2}$

Given, $γ = \frac{5}{3}, C_{p} = 5 R / 2; C_{v} = 3 R / 2$

$\frac{3 R}{2} d T_{1} + R d T_{1} = \frac{3 R}{2} d T_{2}$
$d T_{2} = \frac{5 d T_{1}}{3} = \frac{5}{3} (42) = 70 K$
Option D.

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