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Thermodynamic Processes

Two moles of ...

Question

Two moles of an ideal gas at $300 K$ were cooled at constant volume so that the pressure is reduced to half the initial value. Then as a result of heating at constant pressure, the gas expands till it attains the original temperature. Find the total heat absorbed by the gas, if $R$ is the gas constant.

A

150 R J

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B

300 R J

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C

75 R J

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D

100 R J

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Solution

The correct option is A $300 R J$
In isochoric process $P \propto T$
If pressure halves, temperature halves.
Heat released during isochoric process= $n C_{V} (T_{2} - T_{1}) = 2 \times (\frac{3}{2} R) (300 - 150) J = 450 R J$
Heat absorbed during isobaric expansion= $n C_{P} R (T_{3} - T_{2}) = 2 \times (\frac{5 R}{2}) (300 - 150) J = 750 R J$
Thus net heat absorbed= $300 R J$

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