Question

A certain amount of gas of volume $V$ at $27^{\circ} C$ temperature and pressure $2 \times 10^7 Nm ^{-2}$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use $\gamma=1.5$ )

• A. $3.536 \times 10^5 Pa$
• B. $3.536 \times 10^6 Pa$
• C. $1.25 \times 10^6 Pa$
• D. $1.25 \times 10^5 Pa$

Answer 1

Answer: (B)

$ P _1=2 \times 10^7 Pa $
$P _1 V _1= P _2 V _2$
Since $V_2=2 V_1$ Hence $P_2=P_1 / 2$ (isothermal expansion)
$ P_2=1 \times 10^7 Pa $
$ P_2\left(V_2\right)^\gamma=P_3\left(2 V_2\right)^\gamma$
$P_3=\frac{1 \times 10^7}{2^{1.5}}=3.536 \times 10^6$