Show that entropy is a property of system.

Mumbai university > MECH > SEM 3 > THERMO

Marks: 4M

Year: Dec 2013

1 Answer
  • In order to prove that entropy is a property, we will suppose two cycles i.e. 1-A-2-B-1 and 1-A-2-C-1 as shown in

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  • For a reversible cycle 1-A-2-B-1:

$$\int_{1-A-2}\frac{∂Q}{T} + \int_{2-B-1}\frac{∂Q}{T} = 0$$

  • For a reversible cycle 1-A-2-C-1: $$\int_{1-A-2}\frac{∂Q}{T} + \int_{2-C-1}\frac{∂Q}{T} = 0$$

  • Therefore $$\int_{2-B-1}\frac{∂Q}{T} = \int_{2-C-1}\frac{∂Q}{T} $$

  • Hence, $\int\frac{∂Q}{T}$ is a definite quantity independent of the path followed for the change and depend only upon the initial and the final states of the system.

  • Hence entropy is a property.

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