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 determine the temperature required to double the gas pressure at constant volume, Charles's Law, derived from the Ideal Gas Law, is applied: \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \). In this equation, \(P_1\) denotes the initial pressure, \(T_1\) represents the initial temperature in Kelvin, \(P_2\) signifies the final pressure, and \(T_2\) is the final temperature in Kelvin. The initial state is given as 27°C, which converts to 300K using the formula \(T(K) = T(°C) + 273\). The objective is to achieve double the initial pressure, meaning \(P_2 = 2P_1\). Rearranging the formula to solve for \(T_2\): \[ \frac{P_1}{300} = \frac{2P_1}{T_2} \] Simplifying this equation yields: \[ T_2 = 2 \times 300 = 600 \, \text{K} \] Converting the final temperature back to Celsius using \(T(°C) = T(K) - 273\): \(T_2 = 600 - 273 = 327°C\). Therefore, a temperature of 327°C is necessary to double the gas pressure.