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Question
A system goes from P to Q by two different paths in the P-V diagram as shown in figure. Heat given to the system in path 1 is 1000 J. The work done by the system along path 1 is more than path 2 by 100 J. What is the heat exchanged by the system in path 2?
Solution
According to the first law of thermodynamics,
∆Q = AU + ∆W.
Let us apply this for each path.
For path 1: Heat given Q1 = + 1000 J
Let work done for path 1 = W1
For path 2: Work done (W2) = (W1 – 100) J
Heat has given Q2 = ?
A change in internal energy between two states for the different paths is the same.
∴ ∆U = Q1 – W1 = Q2 – W2
1000 – W1 = Q2 – (W1 – 100)
⇒ Q2 = 1000 – 100 = 900 J
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