An insulated cylinder of volume $60 \mathrm{~cm}^3$ is filled with a gas at $27^{\circ} \mathrm{C}$

Question

An insulated cylinder of volume $60 \mathrm{~cm}^3$ is filled with a gas at $27^{\circ} \mathrm{C}$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20 \mathrm{~cm}^3$ while allowing the temperature to rise to $77^{\circ} \mathrm{C}$. The final pressure is $\_\_\_\_$ atmospheric pressure.

Professor PC Thomas Classes · Answer

Using the ideal gas equation of state $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$. The initial conditions are $P_1 = 2 	ext{ atm}$, $V_1 = 60 	ext{ cm}^3$, and $T_1 = 27^\circ	ext{C} + 273 = 300 	ext{ K}$. The final conditions are $V_2 = 20 	ext{ cm}^3$ and $T_2 = 77^\circ	ext{C} + 273 = 350 	ext{ K}$. Substituting these values into the equation yields $\frac{2 	imes 60}{300} = \frac{P_2 	imes 20}{350}$. Simplifying gives $0.4 = \frac{P_2 	imes 20}{350} \Rightarrow P_2 = \frac{0.4 	imes 350}{20} = \frac{140}{20} = 7 	ext{ atm}$.