Below is a graph of pressure vs. volume. The pressure of state A is 2.5 times th
ID: 488130 • Letter: B
Question
Below is a graph of pressure vs. volume. The pressure of state A is 2.5 times the pressure of state D. In the process of taking a gas from state A to state C along the curved path shown, 80 J of heat leaves the system and 55 J of work is done on the system. When the gas is taken along the path C rightarrow D rightarrow A, the work done by the gas is 38 J. a) How much heat is added to the gas when it is taken through the path C rightarrow D rightarrow A? (Tip: recall that delta E is a state function.)Explanation / Answer
According to first law of thermodynamics, we know
U = q +w
Where U = change in internal energy
q = heat absorbed or heat evolved
w = work done on the system or work done by the system
While taking the system from A to C
q, heat evolved = -80 J
w, work done on the system = 55 J
Thus change in internal energy is
U1 = -80 + 55
= -25 J
As change in internal energy is a state function (it only depends on initial and final state, not on path through which it is attained)
While taking the system from C to D to A, change in internal energy depends on initial and final state only.
Taking a system from C to A
U2 = - U1 = 25 J
w, work done by the system = -38 J
U2 = q + w
Thus q = U2 – w
= 25 – (-38) = 63 J
Thus while taking the system from C to D to A requires 63 J of heat (added to the gas)
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