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The average degree of freedom per molecule of a gas is 6. The gas performs 25J of work in a process when it is expanded at constant pressure. If the amount of heat absorbed by the gas is 25 × X , then the values of X is _______

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answer is 4.

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Detailed Solution

$dQ = {nc}_{p} dt = dQ = n 4 RdT$
$f = 6, C_{p} (1 + f / 2) R = (1 + \frac{6}{2}) R = (1 + 6 / 2) R = 4 R$
$= 4 nRdT = 25 \Rightarrow 4 dw = 4 (25) = x . 25$
$x = 4$

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The average degree of freedom per molecule of a gas is 6. The gas performs 25J of work in a process when it is expanded at constant pressure. If the amount of heat absorbed by the gas is 25 × X , then the values of X is _______