A monatomic gas at pressure P1 and volume V1 is compressed adiabatically to 1/8th of its original volume. What is the final pressure of the gas? (a) 64P1 (b) P1 (c) 16P1 (d) 32P1

Answer: (d). Adiabatic: P₁V₁γ = P₂V₂γ, monatomic γ = 5/3. P₂ = P₁((V₁)/(V₂))γ = P₁ (8)5/3 85/3 = 2⁵ = 32 So the answer is (d) 32P₁.

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Q242NEET 2010 · AIPMT · MAINSEasy

Thermodynamic Processes

A monatomic gas at pressure P1 and volume V1 is compressed adiabatically to ${\frac{1}{8}}^{\text{th}}$ of its original volume. What is the final pressure of the gas?

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Answer: (d)

Adiabatic: $P_1V_1^{\gamma} = P_2V_2^{\gamma}$ , monatomic $\gamma = \frac{5}{3}$ .
$P_2 = P_1\left(\frac{V_1}{V_2}\right)^{\gamma} = P_1 (8)^{5/3}$
$8^{5/3} = 2^5 = 32$
So the answer is (d) $32P_1$ .

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