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

<p>To solve this problem, we can use the combined gas law in terms of pressure ($P$) and temperature ($T$). For a gas with a fixed volume, the relationship is given as:</p> <p>$\frac{P_1}{T_1} = \frac{P_2}{T_2}$</p> <p>where:</p> <p><p>$ P_1 $ is the initial pressure,</p></p> <p><p>$ T_1 $ is the initial temperature in Kelvin,</p></p> <p><p>$ P_2 $ is the final pressure,</p></p> <p><p>$ T_2 $ is the final temperature in Kelvin.</p></p> <p>Given that the initial temperature $ T_1 = 27°C $, we need to convert it to Kelvin:</p> <p>$T_1 = 27°C + 273.15 = 300.15 \, \text{K}$</p> <p>The final pressure $ P_2 $ is twice the initial pressure ($ P_2 = 2P_1 $). Substituting these values into the gas law equation gives:</p> <p>$\frac{P_1}{300.15} = \frac{2P_1}{T_2}$</p> <p>Solving for $ T_2 $:</p> <p><p>Cancel $ P_1 $ from both sides:</p> <p>$\frac{1}{300.15} = \frac{2}{T_2}$</p></p> <p><p>Rearrange to solve for $ T_2 $:</p> <p>$T_2 = 2 \times 300.15 = 600.3 \, \text{K}$</p></p> <p>Convert the final temperature back to Celsius:</p> <p>$T_2 = 600.3 \, \text{K} - 273.15 = 327.15°C$</p> <p>Therefore, to double the pressure of the gas, the temperature should be raised to approximately <strong>327°C</strong>.</p>