A gas is compressed and during this process the surroundings do 84.1 J of work on the gas. At the same time, the gas absorbs 167 J of heat from the surroundings. What is the change in the internal energy of the gas?

Explanation:

Hello,

In this case, we consider the first law of thermodynamics:

Since the gas is absorbing heat it turns out negative as well as the work since the surroundings do work on it; in this manner:

Best regards.

See explanation below

Explanation:

First to all, we need to know the expression to use.

We need to know the change in the internal energy of the gas. This is called ΔU and can be calculated using:

ΔU = q + W   (1)

We have the heat, which is absorbed by the gas from the surroundings. This means that this value is negative. The work is done by the surroundings, so this value is also negative.

All we have to do now is replace the given values into the expression (1), to get the final result:

Replacing the data we have:

ΔU = (-84.1) + (-167)

ΔU = -251.1 J

This would be the change in the internal energy of the gas.

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