Second law limitations on the maximum horsepower output from any power unit burning 1,000,000 BTU/hr of fuel with high and low temperature extremes of 1540 deg. F and 40 deg. F is?

Given:

Power Unit burning = 1,000,000 BTU/hr

High Temperature = 1540 deg. F Low Temperature = 40 deg. F

Power output = ?

Solution:

efficiency = Power output / Power unit burning

efficiency = (High Temp. – Low Temp)(change in entropy) / High Temp (change in entropy) efficiency = (High Temp. – Low Temp)(~~change in entropy~~) / High Temp (~~change in entropy~~)

efficiency = (High Temp. – Low Temp / High Temp

High Temp. absolute = 1540 +460 = 2000 R

Low Temo. absolute = 40+460 = 500 R

*note: All temperatures are in absolute values*

[(High Temp. – Low Temp.) / High Temp.] = Power output / Power unit burning

Power output = [(High Temp. – Low Temp.) / High Temp.] (Power unit burning)

Power output = [(2000 - 500)/2000](1,000,000 Btu/hr)

Power output = (0.75)(1,000,000 Btu/hr)

Power output = 750,000 Btu/hr

Power output = (750,000 Btu/hr)( 1 Horsepower / 2545.5 Btu/hr)

Power output = 294.64 Horsepower (answer)