Question

A container of fixed volume contains a gas at 27°C. To double the pressure of the gas, the temperature of the gas should be raised to °C.

Hint:

To double the pressure at constant volume, the temperature must be doubled in absolute terms (Kelvin scale).

Answer 1

Correct Answer: 327

To solve the problem of determining the temperature needed to double the pressure of a gas within a fixed volume, we apply the Ideal Gas Law in the form of Charles's law, which is given by:
\( \frac{P_1}{T_1} = \frac{P_2}{T_2} \)
Here, \(P_1\) is the initial pressure, \(T_1\) is the initial temperature in Kelvin, \(P_2\) is the final pressure, and \(T_2\) is the final temperature in Kelvin.
The initial condition is at 27°C, which is 300K (since \(T(K) = T(°C) + 273\)). We aim to double the pressure (\(P_2 = 2P_1\)).
Solving for \(T_2\):
\[ \frac{P_1}{300} = \frac{2P_1}{T_2} \]
By simplifying, we find:
\[ T_2 = 2 \times 300 = 600 \, \text{K} \]
Convert back to Celsius: \(T(°C) = T(K) - 273\):
\(T_2 = 600 - 273 = 327°C\).
Thus, the temperature should be raised to 327°C to double the pressure.