300 J of heat was transferred to a monatomic gas located under a piston in a horizontally located cylinder.

300 J of heat was transferred to a monatomic gas located under a piston in a horizontally located cylinder. The piston moves within the cylinder without friction. What is the change in the internal energy of the gas?

The first law of thermodynamics:
The amount of heat transferred to the gas is equal to the sum of the change in the internal energy of the gas and the work done by the gas:
Q = ∆U + A
We find the change in internal energy from the expression:
∆U = (3/2) νR∆T
Gas perfect work:
A = p * ∆V
Let’s substitute all this in the first law of thermodynamics:
Q = ∆U + A = (3/2) νR∆T + p * ∆V
Mendeleev-Clapeyron equation
pV = (m / M) * R * T, where p is the gas pressure, V is the gas volume, m is the gas mass, M is the molar mass of the gas, R is the universal gas constant 8.31 J / (mol * K), T is the gas temperature.
Our piston can move without friction, which means that the pressure is constant, we write down before and after the heat transfer, and taking into account that ν = m / M:
pV1 = ν * R * T1
pV2 = ν * R * T2
pV2-pV1 = ν * R * T2-ν * R * T1
p * ∆V = ν * R * ∆T
Let’s substitute this into the expression of the first law of thermodynamics:
Q = (3/2) νR∆T + p * ∆V = (3/2) νR∆T + ν * R * ∆T = ∆U + 2 * ∆U / 3 = 5 * ∆U / 3
∆U = 3 * Q / 5
Substitute the numbers and find the change in gas energy:
∆U = 3 * Q / 5 = 3 * 300/5 = 180 J.
Answer: the internal energy of the gas has changed by 180 J.