Answer to Question #97475 in Thermal Power Engineering for Syah

Question

Many household use common hot water heating system which delivers hot water to the radiators at 60.0'c. Then, the water leaves the radiators at 28.0'c. New, heating system utilizes steam which at atm pressure condenses in the radiator. Then, the condensed steam leaves the radiators at 35.0'c. How many kg of steam must be produced the same amount of heat supplied by 1.00 kg of hot water?

Answer 1

The heat lost by water, is the heat that the radiators gain

The heat lost by steam, must be equal to the heat lost by water, so the radiators will be supplied the same heat.

Heat lost by water = $mc\Delta T$ = 1000*c*(60-28) = 32000*1 = 32000 calories ...........(1)

Heat supplied by the steam =m*540+m*(100-35)*1 .......(2)

equation 1 must be equal to equation 2

$\implies$ $540m+65m = 32000$

$\implies$ $m=32000/605$

$\implies$ $m= 53 grams$ or $0.053 kg$