Question

1. Suppose the work done to compress a gas is 100 J. If 70 J of heat is lost in the process, what is the change in the internal energy of the gas? Hint: Use the first law of thermodynamics. The internal energy of a system changes due to heat (Q) and work (W): U=Q-W. The change in internal energy is equivalent to the difference between the heat added to the system and the work done by the system. Think if the work done is to the system or by the system. This determines the sign of W.

Answer 1

As already mentioned in the hint section, solve this problem using first law of thermodynamics.

= Q - W

where -

is the variation of internal energy of the gas

Q is the heat absorbed by the gas (this will be positive if heat is absorbed and negative if heat is released by the gas)

W is the work done by the gas (positive if work is done by the gas on the surroundings and negative if work is done by the surroundings)

As mentioned in the problem, work done by the gas, W = -100 J (This is because piston compresses the gas so work is done by the surrounding)

Q = -70 J (The sign is negative because heat is lost by the gas)

Therefore, change in the internal energy of the gas, = Q - W = -70 - (-100) = -70 + 100 = +30.0 J

So, gas has gained 30.0 J of internal energy in the process. (Answer).