How much has the internal energy of the gas changed, which has done work of 50 kJ

How much has the internal energy of the gas changed, which has done work of 50 kJ, having received the amount of heat 85 kJ?

Given:

Q1 = 50 kJ – the amount of work done by the gas;

Q2 = 85 kJ – the amount of heat that the gas received before the work was done.

It is required to determine dQ (Joule) – how much the internal energy of the gas has changed.

Let Q be the value of the initial internal energy of the gas.

Then, after receiving heat, its energy will be equal to:

A1 = Q + Q2.

After completing the work, its energy will be equal to:

A2 = A1 – Q1 = Q + Q2 – Q1

That is, the change in gas energy will be equal to:

dQ = A2 – Q = Q + Q2 – Q1 – Q = Q2 – Q1 = 85 – 50 = 35 kJ = 35000 Joules.

Answer: The internal energy of the gas has increased by 35,000 Joules.