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(C) The fraction of heat energy used to change the internal energy at constant pressure is given by the ratio $\frac{\Delta U}{\Delta Q}$.Since $\Delt

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Fractional energy used to change internal energy is maximum in triatomic gases.

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(C) The fraction of heat energy used to change the internal energy at constant pressure is given by the ratio $\frac{\Delta U}{\Delta Q}$.Since $\Delta Q = n C_P \Delta T$ and $\Delta U = n C_V \Delta T$,we have:$\frac{\Delta U}{\Delta Q} = \frac{n C_V \Delta T}{n C_P \Delta T} = \frac{C_V}{C_P} = \frac{1}{\gamma}$.For a monatomic gas,$\gamma = \frac{5}{3}$,so $\frac{\Delta U}{\Delta Q} = \frac{1}{5/3} = \frac{3}{5} = 0.60$.For a diatomic gas,$\gamma = \frac{7}{5}$,so $\frac{\Delta U}{\Delta Q} = \frac{1}{7/5} = \frac{5}{7} \approx 0.71$.For a triatomic gas (non-linear),$\gamma = \frac{4}{3}$,so $\frac{\Delta U}{\Delta Q} = \frac{1}{4/3} = \frac{3}{4} = 0.75$.Comparing the values,$0.75 > 0.71 > 0.60$. Thus,the fractional energy used to change internal energy is maximum in triatomic gases.

Column-$I$	Column-$II$
$(a)$ Monoatomic gas	$(i)$ ${C_P} = \frac{3}{2}R$
$(b)$ Diatomic gas with vibration	$(ii)$ ${C_P} = \frac{5}{2}R$
	$(iii)$ ${C_P} = \frac{7}{2}R$
	$(iv)$ ${C_P} = \frac{9}{2}R$

$A$ triatomic,diatomic,and monatomic gas are supplied the same amount of heat at constant pressure. Then:

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