As a hot air balloon cools down it is compressed by the air around it. For this process, identify the sign of the heat, the change in internal energy and the work.

All the three of them are negative

Explanation:

We can answer this question by analzying separately the three quantities involved (heat, change in internal energy and work).

Work:

The work done by the gas in the balloon ON the surroundings is

where p is the pressure of the gas and the change in volume.

Here, the gas in the balloon is compressed: this means that the volume is decreasing, so

And therefore,

Where negative work means that the work is done BY the surroundings on the balloon.

Internal energy:

The internal energy of a gas depends solely on its temperature, so the change in internal energy of the gas in the balloon is directly proportional to the change in temperature:

Here, the hot air in balloon is cooled down: this means that the temperature decreases, so the internal energy decreases as well:

Heat:

According to the 1st Law of Thermodynamics,

where Q is the heat absorbed (or released) by the gas.

The equation can be rewritten as

From the previous parts, we have said that both the change in internal energy and the work done by the gas are negative: therefore, the heat must be negative as well (so, heat is released by the gas to the surroundings), so