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Pressure and Temperature

A fixed mass ...

Question

A fixed mass of helium gas is made to undergo a process in which its pressure varies linearly from 1 kPa to 2 kPa, in relation to its volume as the latter varies from $0.2 m^{3}$ to $0.4 m^{3}$ . The heat absorbed by the gas will be

A

300 J

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B

900 J

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C

1200 J

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D

1500 J

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Solution

The correct option is C 1200 J
$Δ W = \frac{1}{2} (1 + 2) \times 10^{3} N / m^{3} \times (0.4 - 0.2) m^{3} = 300 J Δ U = n C_{v} Δ T = \frac{(P_{2} V_{2} - P_{1} V_{1})}{γ - 1} = \frac{3}{2} (0.4 \times 2 - 0.2 \times 1) \times 10^{3} J = 900 J Δ Q = Δ W + Δ U = 1200 J$

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