Question 955: Thermodynamics & KTG

Question

A monoatomic gas of pressure $$p$$ having volume $$V$$ expands isothermally to a volume $$2V$$ and then adiabatically to a volume $$16 \mathrm{~V}$$. The final pressure of the gas is (ratio of specific heats $$=\frac{5}{3}$$

Accepted Answer

In isothermal expansion,
$$\begin{aligned}
& p_1 V_1=p_2 V_2 \
& \Rightarrow \quad p V=p_2(2 V) \Rightarrow p_2=\frac{p}{2}
\end{aligned}$$
In adiabatic expansion,
$$p_2 V_2^\gamma=p_3 V_3^\gamma$$
For monoatomic gas, $$\gamma=\frac{5}{3}$$
$$\begin{aligned}
& \Rightarrow \quad \frac{p}{2}(2 V)^{\frac{5}{3}}=p_3(16 V)^{\frac{5}{3}} \
& \Rightarrow \quad p_3=\frac{p}{2} 	imes \frac{1}{8^{\frac{5}{3}}}=\frac{p}{2 	imes 2^5}=\frac{p}{64}
\end{aligned}$$

Answer

$$\frac{p}{8}$$

Answer

$$\frac{p}{16}$$

Answer

$$\frac{p}{64}$$

Answer

$$\frac{p}{32}$$

Thermodynamics & KTG

A monoatomic gas of pressure $p having volume V expands isothermally to a volume 2V and then adiabatically to a volume 16 \mathrm{~V}. The final pressure of the gas is (ratio of specific heats =\frac{5}{3}

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