Chapter 24, Problem 16A

If all friction could be removed from a heat engine, would it be 100% efficient? Explain.

To determine

Efficiency of heat engine after removing all frictions.

Explanation of Solution

Introduction:

As per the second law of thermodynamics, the heat transfers from a body at high temperature spontaneously to a body at lower temperature. Any device that transforms internal energy to mechanical work is called a heat engine.

Three processes that occur in every heat engine are:

1. The internal energy increases by absorbing energy from hot reservoir.
2. Some of the energy is converted into work.
3. The remaining energy is expelled as heat to cold reservoir.

The thermal efficiency can be expressed as follows:

  $\eta =\frac{W}{Q_H}$

Where,

W is the useful work,

Q_H is the net heat input from the hot source.

As per second law of thermodynamics, it is not possible for heat engines to have $100\%$ thermal efficiency ( $\eta =1$ ). This is because some waste heat is always generated.

The ideal efficiency $\eta$ is:

  $\eta =1-\frac{T_{low}}{T_{high}}$

Even if all friction is removed, $T_{low}=0\text{K}$ cannot be reached and sothe second term cannot be eliminated which implies that $100\%$ efficiency cannot be achieved.