An insulated cylinder of volume 60 cm^3 is filled with a gas at 2… — Solution | JEE Physics

NVAEasyJEE 2026Equation of State of Ideal Gas

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

Answer

Correct answer:7

Step-by-step solution

Standard Method

Given: $V_1 = 60\,\text{cm}^3$ , $P_1 = 2$ atmospheric pressure, $T_1 = 27^\circ\text{C}$ , $V_2 = 20\,\text{cm}^3$ , $T_2 = 77^\circ\text{C}$ .

Find: Final pressure $P_2$ in atmospheric pressure.

Step 1: Convert temperatures to Kelvin.

T_1 = 27 + 273 = 300\,\text{K}, \quad T_2 = 77 + 273 = 350\,\text{K}

Step 2: Apply combined gas law.

\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}

Step 3: Substitute given values.

\frac{2 \times 60}{300} = \frac{P_2 \times 20}{350}

\Rightarrow P_2 = \frac{2 \times 60 \times 350}{300 \times 20} = 7

Therefore, the final pressure is $7$ atmospheric pressure.

Common mistakes

Using temperatures directly in degree Celsius is incorrect because the gas law requires absolute temperature. Convert $27^\circ\text{C}$ and $77^\circ\text{C}$ to $300\,\text{K}$ and $350\,\text{K}$ first.
Using Boyle's law alone is incorrect because the temperature also changes during compression. Use the combined gas law $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$ instead.
Reversing the final and initial volume terms gives the wrong pressure relation. Keep the corresponding states together: $P_1, V_1, T_1$ for the initial state and $P_2, V_2, T_2$ for the final state.

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