Mumbai university > MECH > SEM 3 > THERMO

Marks: 4M

Year: Dec 2013

• 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

• 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.