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  4. To an ideal triatomic gas 800 cal heat energy is given at constant pressure. If vibrational mode is neglected, then energy used by gas in work done against surroundings is

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Q. To an ideal triatomic gas $800$ cal heat energy is given at constant pressure. If vibrational mode is neglected, then energy used by gas in work done against surroundings is

Thermodynamics

Solution:

Heat at constant pressure
$\Delta Q=n C_{P} \Delta T$
Heat for doing work
$\Delta W=n R \Delta T$
Then $\frac{\Delta W}{\Delta Q}=\frac{n R \Delta T}{n C_{P} \Delta T}$
$\frac{\Delta W}{800}=\left(\frac{\gamma-1}{\gamma}\right) $
$\frac{\Delta W}{800}=1-\frac{1}{\gamma}$
$\frac{\Delta W}{800}=1-\frac{3}{4} $
$\Delta W=200 \,cal$