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16. ⇒ (MHT CET 2021 20th September Evening Shift )

A monoatomic gas is suddenly compressed to (1/8)^th of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is ( $γ = 5 / 3$ )

A. 32

B. 8

C. $\frac{40}{3}$

D. $\frac{24}{5}$

Correct Option is (A)

$\frac{V_{2}}{V_{1}} = \frac{1}{8}, γ = \frac{5}{3}$

For adiabatic process,

$\begin{aligned} P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ} \\ ∴ & \frac{P_{2}}{P_{1}} = {(\frac{V_{1}}{V_{2}})}^{γ} = (8)^{5 / 3} = (2)^{5} = 32 \end{aligned}$

17. ⇒ (MHT CET 2021 20th September Morning Shift )

One mole of an ideal gas expands adiabatically at constant pressure such that its temperature $T \propto \frac{1}{\sqrt{V}}$ . The value of $γ$ for the gas is ( $γ = \frac{C_{p}}{C_{v}}, V =$ Volume of the gas)

A. 1.8

B. 1.5

C. 1.3

D. 1.4

Correct Option is (B)

For adiabatic process at constant pressure we have

TV $^{γ - 1}$ = constant ...... (1)

Given $T \propto \frac{1}{\sqrt{V}}$

$∴$ TV $^{1 / 2}$ = constant

By (1) and (2) $γ - 1 = \frac{1}{2}$

$γ = 1.5$

⇒Thermodynamics