Question

Pressure of ideal gas at constant volume is proportional to _______.

• A. average potential energy of the molecules
• B. total energy of the gas.
• C. average kinetic energy of the molecules
• D. force between the molecules

Answer 1

The Correct Option is C

Given: 

• An ideal gas is kept at constant volume.

Step 1: Understanding Pressure in Terms of Molecular Motion

According to the kinetic theory of gases, the pressure of an ideal gas is given by:

\[ P = \frac{2}{3} \left( \frac{N}{V} \right) E_k \]

where \( E_k \) is the average kinetic energy of the molecules.

Step 2: Identifying the Correct Answer

From the equation above, we see that pressure is directly proportional to the average kinetic energy of the molecules.

Answer: The correct option is C.

Answer 2

According to the ideal gas law, the pressure of an ideal gas at constant volume is directly proportional to the temperature of the gas. The temperature of an ideal gas is directly related to the average kinetic energy of the molecules of the gas, as described by the equation: \[ \frac{3}{2} k_B T = \text{average kinetic energy of the molecules} \] where \( k_B \) is the Boltzmann constant and \( T \) is the temperature in Kelvin. At constant volume, if the temperature increases, the average kinetic energy of the molecules increases, which leads to an increase in pressure. Therefore, the pressure of an ideal gas at constant volume is proportional to the average kinetic energy of the molecules.

Thus, the correct answer is option (C): average kinetic energy of the molecules.