Monoatomic gas is kept in equilibrium in an insulated cylinder of length L. Piston is attached with an ideal spring as shown which has relaxed length L. The spring is fixed at one end of cylinder. The gas is supplied very small amount of heat dQ. Piston gets very small displacement in this process. The word done by gas is $\frac{d Q}{N} .$ The value of N is

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answer is 4.

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Detailed Solution

$P A = k x$ and $V = A x \Rightarrow P V = k x^{2} \Rightarrow n R T = k x^{2}$
$d Q = n C_{v} d T + P d V$
= $\frac{3}{2} n R d T + P d V$
= 3kx dx + kx dx = 4kx dx
Work = PdV = kxdx

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