A monatomic gas (v = 2 moles) is transferred to an amount of heat of 1.2 kJ.

A monatomic gas (v = 2 moles) is transferred to an amount of heat of 1.2 kJ. while the gas does work 600 J. How much will the gas temperature change?

Let’s translate all the values from given to the SI system:
Q = 1.2 kJ = 1200 J.
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
Let us express ∆U from this expression:
∆U = Q – A
We find the change in internal energy from the expression:
∆U = (3/2) νR∆T
Let us express the change in temperature from this expression:
∆T = 2 * ∆U / (3 * ν * R)
∆T = 2 * (Q-A) / (3 * ν * R)
Substitute the numerical values and calculate the temperature change:
∆T = 2 * (Q-A) / (3 * ν * R) = 2 * (1200-600) / (3 * 2 * 8.31) = 24 K.
Answer: the temperature will change by 24 K or 24 ° C.