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  4. A certain amount of an ideal monatomic gas needs 20 J of heat energy to raise its temperature by 10° C at constant pressure. The heat needed for the same temperature rise at constant volume will be

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Q. A certain amount of an ideal monatomic gas needs $20\, J$ of heat energy to raise its temperature by $10^{\circ} C$ at constant pressure. The heat needed for the same temperature rise at constant volume will be

Thermodynamics

Solution:

$\Delta Q=n C_{P} \Delta T$
$20=n C_{P} \times 10\,\,\,...(1)$
$\Delta U=n C_{V} \Delta T$
$\Delta U=n \frac{C_{P}}{\gamma} \Delta T$
$\left\{\because \gamma_{\text {mono }}=5 / 3\right\}$
$\Delta U=12 \,J$