Question

A gas expands and does 95.4 J of work on the surroundings. At the same time, the gas loses 250 J of energy to the surroundings as heat. What is the change in the internal energy of the gas?

Answer 1

According to the first law of thermodynamics " Energy can neither be created nor destroyed but it can be converted from one form to another via interaction of heat, work and internal energy ."

Mathematically, the first law is given by the relation :

∆U = q + w

where ∆U is the change in internal energy, q is heat exchange between the system and the surroundings and w is work done by/on the system.

The sign conventions for heat and work are :

When work is done on the system, w is positive.

When work is done by the system , w is negative.

When heat is released by the system , q is negative.

When heat is absorbed by the system , q is positive.

Now in the given question , using these sign conventions we have

Work done by the system (gas) on the surroundings (w) = -95.4 J

Heat lost by the system (gas) to the surroundings (q) = -250 J

So the change in internal energy of the gas ( ∆U ) = q + w

Thus ∆U = (-250 J) + (-95.4 J) = ( -250 -95.4 ) J = -345.4 J

So change in internal energy of the gas is -345.4 J .