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Sheet 1

Thermodynamics 2

Carnot cycle

Calculate the Carnot cycle efficiency for a cycle running betvleen 300 and 1000 K. lf

the heat input rate to the cycle is 450kW, calculate the max power output.

Calculate the thermal efficiency of a Carnot cycle heat engine operating between

500"C and 40"C.

A car'engine burns 5 kg fuel at 1500 K and rejects energy to the radiator and

exhausts at 750 K. If the fuel provides 40 MJ/kg, what is the max amount of wok the

engine can provide?

We propose to heat a house in the winter with a heat pump. The house is to be

maintained at 20"C at all times. When the ambient temperature outside drops to -

10oC, the rate at which heat is lost f rom the house is estimated to be 25 kW. What is

the minimum electrical power required to drive the heat pump?

A thermal storage device is made with a rock bed of 2 m3 that is heated to 400 K

using solar energy. A heat engine receives QH from the bed and rejects heat to the

ambient surroundings at 290 K. The rock bed therefore cools down, as it reaches

29O K the process stops. Find the energy the rock can give out. What is the heat

engine efficiency at the beginning of the process, and what is it at the end of the

process? You may assume that the density and the specific heat for rock is g = 2750

kgim3 and C = 0.89 kJ/kg-K, respectively.

A car engine operates with a thermal efficiency of 35"/". Assume the air conditioner

has a coefficient of performance of F=3 working as a refrigerator cooling inside using

engine shaft work to drive it. How much extra fuel energy should be spent to remove

1 kJ from the inside?

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