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Consider the cyclic process depicted below.
What are the signs of Q , W_{done}_{ on}, and ΔE_{int} that are associated with each process, and for the process as a whole?
Q | W_{ongas} | ΔU (ΔE_{int}) | |
A to B | |||
B to C | |||
C to A | |||
Complete |
From A to B: The gas is heated to increase its volume and pressure, so Q is positive and ||W=-P\Delta V|| is negative. Temperature increases so ||\Delta U|| is positive.
From B to C: Work is zero since ||\Delta V=0||. Need to cool it to reduce pressure and the temperature also drops on the PV diagram (from an isothermal line with higher temperature to an isothermal line with lower temperature). So Q is negative and ||\Delta U|| is negative.
From C to A: The gas is cooled to decrease its volume, so Q is negative and ||W=-P\Delta V|| is positive. Temperature also decreases so ||\Delta U|| is negative.
For the whole cycle considering from A to B to C and back to A. The total work on the gas is negative: the work done in AB is negative and the work done in CA is positive. But the magnitude of the work in AB is larger than that is CA, so the total work to gas is negative (another way to think about this is that the gas is doing positive work to the environment).
For a complete cycle, the internal energy doesn't change (same temperature), therefore, ||\Delta U=0||. Since ||\Delta U=Q+W||, Q must be larger than zero because W is negative.
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Q | W_{ongas} | ΔU (ΔE_{int}) | |
A to B | + | - | + |
B to C | - | 0 | - |
C to A | - | + | - |
Complete | + | - | 0 |