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A particular power plant operates with a heat-source reservoir at 350°C and a heat-sink reservoir at...

A particular power plant operates with a heat-source reservoir at 350°C and a heat-sink reservoir at 30°C. It has a thermal efficiency equal to 67% of the Carnot-engine thermal efficiency for the same temperatures.

What is the thermal efficiency of the plant?

The thermal efficiency of the plant is .

Expert Solution

Particular power plant operates with heat source reservoir Temperature Th = 350 C = 350 + 273 = 623 K

Heat sink reservoir temperature TL = 30 C = 30 + 273 = 303K

Carnot engine cycle - Carnot engine gives maximum efficiency. It is based on second law of thermodynamics. Carnot engine is used to transfer heat from higher to lower temperature by converting some amount of work. By second law of thermodynamics heat can not be fully converted into work.

If we give heat from heat reservoir source is Qh and engine transfer to the sink reservoir QL by converting W work then,

Carnot engine efficiency = work output /heat input = W/Qh

Where W = Qh - QL

By entropy relation, Qh = Th*ΔS

QL = TL*ΔS

Efficiency = Qh-QL/Qh = 1- QL/Qh = 1- TL*ΔS/Th*ΔS = 1- TL/Th

Carnot engine efficiency = (1- TL/Th)*100

= (1-303/623)*100 = 51.36 %

Given power plant operates with thermal efficiency equal to 67% of carnot engine efficiency.

power plant thermal efficiency = 0.67*51.36 = 34.41%

Ans: 34.41 %

Amanda K answered 6 months ago

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