GATE 2026 MT – Question 55
The constant-pressure molar heat capacity of a solid metal is $C_p=20+(5\times10^{-3})T\ \mathrm{J/(mol\,K)}$ for $298\le T\le1000\ \mathrm K$. At constant pressure, the temperature of 2 moles is increased from 300 K to 600 K. The enthalpy change is ________ J. (Answer in integer.)
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Correct answer: 13340 to 13360
Explanation
At constant pressure, $\Delta H=n\int_{300}^{600}C_p(T)\,dT$. Integration gives $\Delta H=2[20(600-300)+(5\times10^{-3}/2)(600^2-300^2)]$.
Thus $\Delta H=2(6000+675)=$ **13350 J**. Integrating the varying heat capacity avoids treating it as constant.