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  4. An ideal gas with adiabatic exponent γ is heated at constant pressure. It absorbs Q amount of heat. Fraction of heat absorbed in increasing the temperature is

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Q. An ideal gas with adiabatic exponent $\gamma$ is heated at constant pressure. It absorbs $Q$ amount of heat. Fraction of heat absorbed in increasing the temperature is

Thermodynamics

Solution:

Heat absorbed in increasing temperature $=\Delta U=\Delta Q-\Delta W=n C_{V} \Delta T$
Fraction of heat absorbed $=\frac{\text { Heat absorbed }}{\text { Total heat }}$
$=\frac{n C_{V} \Delta T}{n C_{P} \Delta T}$
$=\frac{C_{V}}{C_{P}}=\frac{1}{\gamma}$