How will the efficiency of an ideal heat engine change, in which the temperature of the heater

| September 8, 2021 | education

How will the efficiency of an ideal heat engine change, in which the temperature of the heater is twice the temperature of the refrigerator, if, without changing the temperature of the heater, the temperature of the refrigerator is halved?

Given:

Tн is the temperature of the heater of an ideal heat engine;

Tх1 is the temperature of the cooler of an ideal heat engine;

Tн = 2 * Tx1 – the heater temperature is twice the temperature of the refrigerator;

Tx2 = Tx1 / 2 – the temperature of the refrigerator was reduced by 2 times.

It is required to determine n2 / n1 – how the efficiency of the ideal motor of a heat engine will change.

The efficiency of the engine in the first case will be equal to:

n1 = (Tn – Tx1) / Tn = (2 * Tx1 – Tx1) / (2 * Tx1) = Tx1 / (2 * Tx1) = 1/2 = 0.5.

The efficiency of the engine in the second case will be equal to:

n2 = (Tn – Tx2) / Tn = (2 * Tx1 – Tx1 / 2) / (2 * Tx1) = 3 * Tx1 / (4 * Tx1) = 3/4 = 0.75.

Then:

n2 / n1 = 0.75 / 0.5 = 1.5, that is, the efficiency will increase 1.5 times.

Answer: The efficiency of an ideal engine of a heat engine will increase by 1.5 times.



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