The average kinetic energy of the molecules in a sample of an ideal gas increases with the volume remaining constant. Which of these statements must be true?

(a) The pressure increases and the temperature stays the same.

(b) The number density decreases.

(d) Both the pressure and the temperature increase.

Solutions

Expert Solution

The expression of average kinetic energy is as follows,

(Ktr) = 3/2 ∙ PV/N

= 3/2 kT

Here P is the pressure of the gas, V is the volume of the gas, and N is the number of molecules, k is the

Maxwell-Boltzmann constant and T is the temperature.

From the expression of average translational kinetic energy if volume of the gas is constant the kinetic energy is directly proportional to the pressure or temperature.

Volume is constant therefore the temperature will be directly proportional to the pressure of the gas.

The expression of number density is as follows,

Number density = N/V

Also the number density is directly proportional to the average kinetic energy.

Therefore, option (a), (b) and (c) is incorrect.

Pressure of the gas and temperature is directly proportional to each other if the volume of the gas is constant and is directly proportional to the kinetic energy.

Hence option (d) is correct.

The option (d) is correct.

Junaid answered 1 year ago

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