Question

To double the pressure of an ideal gas, keeping volume and number of moles constant, the temperature should be:

• A. 2T
• B. 4T
• C. T/2
• D. T/4

Hint:

Remember, for an ideal gas, pressure and temperature are directly proportional when volume and the number of moles are constant. Doubling the pressure requires doubling the temperature.

Answer 1

The Correct Option is A

For an ideal gas, the relation between pressure, volume, temperature, and number of moles is given by the ideal gas law: \[ PV = nRT \] Where: - \(P\) is the pressure,
- \(V\) is the volume,
- \(n\) is the number of moles,
- \(R\) is the ideal gas constant,
- \(T\) is the temperature. If the volume and number of moles are constant, the equation becomes: \[ P \propto T \] Therefore, to double the pressure, the temperature must also be doubled. Hence, the temperature should be \(2T\). Therefore, the correct answer is option (A).