I came across this question, but I dont really understand the answer. Can someone explain it please?
"A gas in a container with a flexible lid is cooled by ice with 250J of energy extracted. Calculate whether the temperature has increased or decreased."
The answer:
Q = -250 J, W = -250 J, U = 0, no change in temperature
How would I interpret this answer?
Does this mean that the environment has done work on the gas by cooling it (W<0)?
I think that this is a poor question.
The system is the gas in the container.
The flexible lid implies that the volume of the gas can change.
So $250\; \rm J$ of heat is removed from the gas and to keep the internal energy (temperature) of the gas unchanged that loss of heat from the gas must be balanced by $250\; \rm J$ of work done by the surroundings.
With work done by the gas as positive and heat into the gas as positive, using the first law of thermodynamics $\Delta U = \delta Q - \delta W \Rightarrow 0 = -250 - (-250)$ as per the answer.
The gas has not cooled in the sense that its temperature has decreased.
The term cooled as used here means that heat has be extracted from the gas but how is one to know that from the wording of the question?
