Question

cooling a gas in a piston cylinder.

if the boundary work of piston cylinder is compressed

W = -10 kj

determine if it is gained or lost by the gas.

Answer 1

Solution: Let us first brush up some thermodynamics sign convention and then we shall attempt to answer the question in hand.

Relationship between WD and Energy in closed systems is:

Now applying this first law for gas piston system we get, the following table:

Coming to question in hand, as we saw that WD by the system is taken as positive and negative when done on the system. Since WD is given as minus 10 kJ it is the word done on the system (WD by the piston on the gases). (Refer to both the tables). It is gained by the gas.

Alternative Approach:

Let us say that we dont know any thermodynamics laws and wish to analyse the system using our logic and just simple engineering aptitude. Can we still tell whether the Work is done by the system or on the system? YES we can. How? This can be explained by understanding that the gas in the piston cannot compress itself by its own. Right? So to compress it that means to perform compression work(as given in the question) the external system has to compress it, that means it has to do work on the system. Therefore compression WD in piston gas system is always negative and is taken to be WD by the surrounding on the system. And this WD is gained by the system(gas).

I hope this gives some clarity.

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