Mr. White claims that he invented a heat engine with a maximum efficiency of 90%. He measured the temperature of the hot reservoir as 100o C and that of cold reservoir as 10o C. Find the error that he made and calculate the correct efficiency. Hint: The efficiency (e) of a Carnot engine is defined as the ratio of the work (W) done by the engine to the input heat QH : e=W/QH. W=QH – QC, where Qc is the output heat. That is, e=1-Qc/QH =1-Tc/TH, where Tc for a temperature of the cold reservoir and TH for a temperature of the hot reservoir. The unit of temperature must be in Kelvin.

The error he made was that he didn't convert the unit of temperature to Kelvin.

The correct efficiency is 24%

Explanation:

Parameters given:

Temperature of hot reservoir = 100°C = 373 K

Temperature of cold reservoir = 10°C = 273 K

The efficiency of a heat engine is given as:

E = 1 - (Qc/Qh) = 1 - (Tc/Th)

Where

Qc = Output heat;

Qh = Input heat;

Tc = Temperature of the cold reservoir;

Th = Temperature of the hot reservoir.

=> E = 1 - (283/373)

E = 1 - 0.76

E = 0.24

In percentage,

E = 0.24 * 100 = 24%

Hence, the efficiency of the engine is actually 24%.

The error he made was that he didn't convert the temperature to Kelvin. If we leave the temperatures in °C, we have that:

E = 1 - (10/100)

E = 1 - 0.1 = 0.9

In percentage,

E = 0.9 * 100 = 90%

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