(a) What is the efficiency of a cyclical heat engine in which 75.0 kJ of heat transfer occurs to

step 1 So part A asks us to find the efficiency of heat engine. We are given that heat supplied is 95 k

(a) What is the efficiency of a cyclical heat engine in...

(a) What is the efficiency of a cyclical heat engine in which $75.0 \mathrm{kJ}$ of heat transfer occurs to the environment for every $95.0 \mathrm{kJ}$ of heat transfer into the engine? (b) How much work does it produce for $100 \mathrm{kJ}$ of heat transfer into the engine?

Key Concepts

Thermal Efficiency

Thermal efficiency is a measure of a heat engine's performance and is defined as the ratio of work output to heat input. It indicates how effectively a heat engine converts thermal energy into useful mechanical work. In problems involving heat engines, it is calculated by subtracting the fraction of input heat rejected to the surroundings from one, or by directly using the formula ? = W/Q_in.

Heat Engine

A heat engine is a device that converts heat energy into mechanical work via a series of thermodynamic processes. It operates cyclically, meaning it returns to its initial state at the end of each cycle, allowing the process to repeat indefinitely. The energy balance in a heat engine is governed by the conservation of energy, where the net work produced is the difference between the heat added to the system and the heat rejected.

First Law of Thermodynamics

The First Law of Thermodynamics, which is essentially the law of energy conservation for thermodynamic systems, states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In the context of cyclic processes, since the system returns to its original state, the net change in internal energy is zero, and the work output is directly equal to the net heat absorbed (heat input minus heat rejected).

Work Output Calculation

Calculating the work output of a cyclical heat engine involves determining the difference between the heat absorbed and the heat rejected in each cycle. Once the efficiency is known, the work produced for any given heat input can be directly obtained by multiplying the efficiency by the heat input. This concept is crucial for relating theoretical efficiency to practical work output in heat engine operations.

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