Question

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.

Answer 1

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

The correct efficiency is 24%

Step-by-step 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%