JNTU B.Tech II THERMODYNAMICS Previous Question Paper (March - 2021 - R15)

A system is in thermodynamic equilibrium if it satisfies three specific conditions simultaneously: mechanical equilibrium (no unbalanced forces), chemical equilibrium (no chemical reactions or mass transfer), and thermal equilibrium (no temperature gradients). When these conditions are met, the macroscopic properties of the system remain constant over time.

In contrast, thermal equilibrium is a more restricted state where the temperature of the system is uniform throughout and equal to the temperature of its surroundings. While thermal equilibrium is a necessary condition for thermodynamic equilibrium, it is not sufficient on its own. A system can be in thermal equilibrium but remain out of mechanical or chemical equilibrium (e.g., a gas in a cylinder with a piston held by a pin, where pressure is not uniform or chemical reactions are occurring).

To prove that work transfer is a path function, consider a system undergoing a process from state 1 to state 2. Work done is defined as the integral of the product of pressure and change in volume:

If work were a point function (a property), its value would depend only on the initial and final states, and the integral of its differential dW over a closed cycle would be zero. However, consider a gas expanding from state 1 to state 2 along two different paths, A and B:

1. Along path A, the area under the P-V curve represents the work done.
2. Along path B, the area under the curve is different from path A, even though the initial and final states are identical.
3. If the system is taken from state 1 to 2 via path A and returned to state 1 via path B, the net work done for the cycle is the difference between the areas under the two curves, which is non-zero.

Because the net work done in a cycle is not zero, the differential dW is an inexact differential (denoted as δW). This confirms that work depends on the specific path taken between states, making it a path function rather than a state property.