An ideal gas at 27 is compressed adiabatically to 8/27 of its original volume. The rise in temperature is (γ = 5/3) (a) 475 (b) 402 (c) 275 (d) 375

Answer: (d). Adiabatic: T₂ = 300(27/8)2/3 = 300 × 9/4 = 675 K. Rise = 675 - 300 = 375 K; a temperature difference is the same in K and. So the answer is (d) 375.

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Thermodynamic Processes

An ideal gas at $27^\circ\text{C}$ is compressed adiabatically to $\frac{8}{27}$ of its original volume. The rise in temperature is $\left(\gamma = \frac{5}{3}\right)$

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Answer: (d)

Adiabatic: $T_2 = 300\left(\frac{27}{8}\right)^{2/3} = 300 \times \frac{9}{4} = 675\ \text{K}$ .
Rise $= 675 - 300 = 375\ \text{K}$ ; a temperature difference is the same in K and $^\circ\text{C}$ .
So the answer is (d) $375^\circ\text{C}$ .

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