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A system fitted with a piston expands when it absorbs 52.7J of heat from the surroundings. The piston is working against a pressure of 0.693 atm. the final volume is 63.2L. what was the initial volume of the system if the internal energy of the system decreased by 107.4J?

Answer :

Answer: The initial volume of the system is 60.29 L.

Explanation:

According to the first law of thermodynamics,

      [tex]\Delta U = Q - W[/tex]

As it is given that heat is being added to the system so, [tex]\Delta H[/tex] will be positive. And, work done on the system is negative and work done by the system is positive.

So here, [tex]\Delta U[/tex] = -107.4 J

                    Q = 52.7 J

                    P = 0.693 atm

And,     W = PdV

or,        W = [tex]P (V_{final} - V_{initial})[/tex]

So,       [tex]\Delta U = Q - P (V_{final} - V_{initial})[/tex]

            -107.4 J = 52.7 J - 0.693 \times 101.325 (63.2 - V)

            -160.1 = -43.79 - 70.21 (63.2 - V)

           63.2 - V = [tex]\frac{160.1 + 43.79}{70.21}[/tex]

                  - V =  2.90 - 63.2

                     V = 60.29 L

Thus, we can conclude that the initial volume of the system is 60.29 L.

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