Question 49

A container of fixed volume contains a gas at $$27^{\circ}C$$. To double the pressure of the gas, the temperature of gas should be raised to ______ $$^{\circ}C$$.


Correct Answer: 327

We need to find the temperature to which a gas must be raised to double its pressure at constant volume.

For a gas at constant volume, from the ideal gas law:

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

Given: $$T_1 = 27°C = 300 \, K$$, $$P_2 = 2P_1$$.

$$T_2 = T_1 \times \frac{P_2}{P_1} = 300 \times \frac{2P_1}{P_1} = 300 \times 2 = 600 \, K$$

$$T_2 = 600 - 273 = 327°C$$

The answer is 327°C.

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