Thermodynamics

JEE Main level, numerical answer, medium

68 of 190

Question 68 of 190

A diatomic gas (γ=1.4)(\gamma=1.4) does 100 J of work when it is expanded isobarically. Then the heat given to the gas ____\_\_\_\_ J.

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Answer: 350

For an isobaric process, the first law gives: Q=ΔU+WQ = \Delta U + W.
For a diatomic gas with γ=1.4\gamma = 1.4, we have CV=52RC_V = \frac{5}{2}R and CP=72RC_P = \frac{7}{2}R.
Since W=nRΔT=100W = nR\Delta T = 100 J for isobaric expansion, the change in internal energy is: ΔU=nCVΔT=52nRΔT=52×100=250\Delta U = nC_V\Delta T = \frac{5}{2}nR\Delta T = \frac{5}{2} \times 100 = 250 J.
Therefore, Q=250+100=350Q = 250 + 100 = 350 J.

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