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MHT CET · Physics · Thermodynamics

In ideal gas of \(27^{\circ} \mathrm{C}\) is compressed adiabatically to \((8 / 27)\) of its original volume. If \(\gamma=\frac{5}{3}\), the rise in temperature of a gas is

  1. A 300 K
  2. B 375 K
  3. C 400 K
  4. D 450 K
Verified Solution

Answer & Solution

Correct Answer

(B) 375 K

Step-by-step Solution

Detailed explanation

\(\begin{aligned} \therefore \quad \frac{\mathrm{T}_2}{\mathrm{~T}_1} & =\left(\frac{\mathrm{V}_1}{\mathrm{~V}_2}\right)^{\gamma-1} \\ & =\left(\frac{27}{8}\right)^{\frac{5}{3}-1} \quad \ldots\left(\text { given, } \mathrm{V}_2=\frac{8}{27} \mathrm{~V}_1\right) \\ & =\left(\frac{27}{8}\right)^{\frac{2}{3}}=\frac{9}{4} \\ \therefore \quad \mathrm{~T}_2 & =\frac{9}{4} \times \mathrm{T}_1=\frac{9}{4} \times(27+273)=675 \mathrm{~K} \\ \therefore \quad \mathrm{~T}_2 & -\mathrm{T}_1=675-(27+273)=375 \mathrm{~K}\end{aligned}\)
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