An ideal diatomic gas is heated at constant pressure. The ratio of the work done to the heat supplied is
KVPY 2009, Medium
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(c)
Heat supplied at constant pressure is $\Delta Q=n C_p \Delta T$.
Work done by the gas,
$\Delta W=p \Delta V=n R \Delta T$
Ratio of work done to heat supplied is
$\frac{\Delta W}{\Delta Q}=\frac{n R \Delta T}{n C_p \Delta T}$
$=\frac{R}{C_p}=\frac{C_p-C_V}{C_p}$
$=1-\frac{1}{\gamma}$
$=1-\frac{1}{(7 / 5)}=1-\frac{5}{7}=\frac{2}{7}$
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