GATE 2025 BT – Question 29

Fundamentals of Biological Engineering · Bioreaction Engineering: Batch, fed-batch and continuous processes, microbial and enzyme reactors, optimization and scale up · 1 mark · Numerical answer

For a mechanically reversible isobaric process taking place in a closed system involving 5 moles of an ideal gas, the temperature increases from an initial value of 300 K to a final value of 450 K. If the specific heat capacity at constant volume ($C_v$) is given as 12.5 J mol$^{-1}$ K$^{-1}$ and gas constant is 8.314 J mol$^{-1}$ K$^{-1}$, the amount of heat transferred to the system will be ______ J. (Round off to the nearest integer)

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Correct answer: 15611

Explanation

At constant pressure $Q = nC_p\Delta T$ with $C_p = C_v + R = 12.5 + 8.314 = 20.814$ J/mol K. So $Q = 5 \times 20.814 \times 150 = 15610.5 \approx 15611$ J.