JNTU B.Tech IV BASIC MECHANICAL ENGINEERING Previous Question Paper (February/March - 2022 - R18)

A heat engine is a thermodynamic device that operates in a cycle to convert thermal energy into mechanical work. It extracts heat from a high-temperature source, performs work on the surroundings, and rejects the remaining heat to a low-temperature sink.

The operation is governed by the Second Law of Thermodynamics, which dictates that no engine can convert all input heat into work. The efficiency is defined as the ratio of net work output to the heat supplied from the source.

Key components include:

• Source (T_H): A reservoir at a high temperature that supplies heat (Q_H).
• Working Substance: The medium (gas or vapor) that undergoes cyclic expansion and compression.
• Sink (T_L): A reservoir at a lower temperature that absorbs rejected heat (Q_L).
• Work Output (W): The net energy extracted as mechanical work, where W = Q_H - Q_L.

Sketch description: A rectangular box representing the engine connected to a source reservoir at T_H above it and a sink reservoir at T_L below it. An arrow labeled Q_H points from the source into the engine, an arrow labeled W points out of the engine, and an arrow labeled Q_L points from the engine into the sink.

A path function is a thermodynamic quantity whose value depends on the specific process or path taken to transition between two equilibrium states, rather than just the states themselves. Unlike state functions (like internal energy or pressure), path functions are inexact differentials.

To show that heat and work are path functions:

1. Work: Consider a gas expanding from state 1 to state 2. If the process is a constant pressure expansion, the work done is the area under the P-V diagram line. If the process follows a different path (e.g., isothermal or adiabatic), the area under the curve changes significantly. Since the work done depends on the path taken between the same two states, work is a path function.
2. Heat: According to the First Law of Thermodynamics, Q = ΔU + W. For a fixed change in state, the change in internal energy (ΔU) is constant because it is a state function. However, because work (W) is a path function, the heat transfer (Q) required to achieve that state change must also vary depending on the path taken.

Mathematically, the integral of a path function between two states depends on the process: ∫ δW ≠ W_2 - W_1. Therefore, heat and work are represented by inexact differentials (δQ and δW) rather than exact differentials (dQ and dW).