A heat engine works between source and sink temperature150 c and 30 c ...
Efficiency of Heat Engine
A heat engine is a device that converts thermal energy into mechanical energy. The efficiency of a heat engine is the ratio of the work output to the heat input. It is denoted by the symbol η and expressed as a percentage.
Formula for Efficiency
The efficiency of a heat engine is given by the formula:
η = (1 - Ts/Th) x 100%
- η: Efficiency of the heat engine
- Ts: Temperature of the sink
- Th: Temperature of the source
Calculating Efficiency
In this question, the source temperature (Th) is 150°C and the sink temperature (Ts) is 30°C. Using the formula above, we can calculate the efficiency as:
η = (1 - 30/150) x 100% = 80%
Therefore, the efficiency of the heat engine is 80%.
Explanation
The efficiency of a heat engine is limited by the Carnot cycle, which is the most efficient cycle possible between two given temperatures. The efficiency of the Carnot cycle is given by:
ηCarnot = (Th - Ts)/Th
As the temperature of the sink (Ts) decreases, the efficiency of the heat engine increases. However, the efficiency cannot exceed the Carnot efficiency, which is determined by the temperature difference between the source and sink.
In this question, the efficiency of the heat engine is 80%, which is quite high. It means that 80% of the heat energy supplied to the engine is converted into useful work, while the remaining 20% is lost as heat to the surroundings.