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

Given: Volume $$V_1 = 60$$ cm$$^3$$, $$T_1 = 27°C = 300$$ K, $$P_1 = 2$$ atm. Final: $$V_2 = 20$$ cm$$^3$$, $$T_2 = 77°C = 350$$ K.

Using the combined gas law (assuming the gas is sealed):

$$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$$

$$P_2 = P_1 \times \frac{V_1}{V_2} \times \frac{T_2}{T_1} = 2 \times \frac{60}{20} \times \frac{350}{300} = 2 \times 3 \times \frac{7}{6} = 7 \text{ atm}$$

The answer is 7.