Calculation of Efficiency of Carnot's Engine

The efficiency of a Carnot's engine is given by the formula:

Efficiency = (Th - Tc) / Th

where Th is the temperature of the hot body and Tc is the temperature of the cold body.

Given that the efficiency of the engine with Tc = 17 degree C is 50%, we can calculate the value of Th as follows:

50/100 = (Th - 17) / Th

Th = 34 degree C

Effect of Increasing Hot Body Temperature on Efficiency

When the temperature of the hot body is increased by 145 degree C, the new temperature Th' becomes:

Th' = Th + 145 = 34 + 145 = 179 degree C

Using the same formula for efficiency, we can calculate the new efficiency of the engine:

Efficiency' = (Th' - Tc) / Th'

Efficiency' = (179 - 17) / 179

Efficiency' = 90.5%

Explanation

The efficiency of a Carnot's engine is directly proportional to the temperature difference between the hot and cold bodies. Therefore, when the temperature of the hot body is increased, the efficiency of the engine also increases. This is because the engine is able to extract more work from the same amount of heat energy as the temperature difference between the hot and cold bodies is greater.

In this case, the efficiency of the engine increases from 50% to 90.5% when the temperature of the hot body is increased by 145 degree C. This shows that a small increase in temperature can have a significant impact on the efficiency of the engine.