What pressure is exerted by a monatomic ideal gas if it occupies a volume of 20 liters, and its internal energy is 1200 J?

According to the formula for the internal energy of a one-volume ideal gas:

Uin = 3/2 ν * R * T, where ν is the amount of the substance of a given gas, R is the universal gas constant, and T is the temperature.

According to the Mendeleev-Clapeyron equation, known from the physics course:

p * V = v * R * T.

Uin = 3/2 * p * V.

Therefore, the pressure exerted by the gas can be found as:

p = 2/3 * Uin / V.

Let’s substitute the available data into the formula:

p = 2/3 * 1200 J / 20 L = 40 kJ.

Answer: the pressure exerted by a monatomic gas is 40 kJ.