# Efficiency of an Ideal Heat Engine

## Other Skills

• Convert between Celsius and Kelvin temperatures
1. Suppose that the turbines of a coal-fired plant are driven by hot gases at a temperature of 886 K. If the temperature of the exhaust area is only 305 K, what is the efficiency of this heat engine?
2. A given automobile’s engine operates with a combustion temperature of 1600 °C. If the exhaust temperature is 33 °C, what is the greatest possible efficiency of this engine?
3. A power plant’s generation system needs to have an efficiency of 22% when its cold reservoir is maintained at 32 °C. What Kelvin temperature must the hot gases that drive the turbines reach in order to accomplish this?
4. Suppose that the engineers wish for the steam turbine at a nuclear plant to operate at an efficiency of 33.0%. If the steam reaches a temperature of 330 °C, at what Celsius temperature would the cold reservoir need to be maintained in order to achieve the desired efficiency?
5. A heat engine operates between temperatures of 263 K and 585 K. If 4.30 × 103 J of energy are provided as input heat every cycle, how much useful work is done in each cycle?
6. A heat engine is required to accomplish 6.0 × 102 J of useful work each second. If the engine operates between temperatures of 19 °C and 380 °C, how much heat energy must be input each second?

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