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?

Answer 1

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