Thermodynamics1 Please show the work. A steam engine functions by converting liq

Question

Thermodynamics1

Please show the work.

A steam engine functions by converting liquid water to steam, which is then used to drive a rotating shaft. This engine contains two engineering devices: the boiler where the liquid water is converted to steam and the turbine where the steam is used to drive the shaft. Let the fuel used in the boiler be wood with a heating value of 15 MJ/kg (i.e. when 1 kg of wood is burned 15 MJ of energy is released). When 0.1 kg of fuel was burned the shaft output was measured to be 567 kJ. Assuming that the turbine is 90% efficient, what is the efficiency of the boiler?

Explanation / Answer

Total Energy released by burning wood = mass x heating value = 0.1x15 = 1.5 MJ

Now this times the efficieny of the boiler will be the input for the shaft = 1.5*n where n is the efficiency of the boiler. Now the output will be this input times the efficiency of the turbine = 1.5*n*0.9 which equals 567 KJ = 0.567 MJ

n = 0.567/(1.5*0.9) = 0.42 = 42%

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