Question

1. An electric power plant uses energy from burning coal to generate steam at 450 °C. The plant is cooled by 20 °C water

from nearby river. If burning coal provides 100 MJ of heat, what the theoretical minimum amount of heat that must be
transferred to the river during the conversion of heat to electric energy?​

Answer 1

Step-by-step explanation:

Efficiency of the electric power plant is
`e=1-(T_(2))/(T_(1))`

Here Temperature of hot source
`T_(1) = 450^(o)C=450+273=723 K`

and Temperature of sink
`T_(1) = 20^(o)C=20+273=293 K`

Hence the efficiency is
`e=1-(293)/(723)=0.5947=59.47%`

Now another formula for thermal efficiency Is

`e_(therm)=(Q_(1)-Q_(2))/(Q_(1))=(W)/(Q_(1))`

Here QI is the of heat taken from source 100 MJ ; Q2 of heat transferred to the sink (river) to be found

W is the of work done and W = QI -Q2

Hence From
`e_(therm)=(Q_(1)-Q_(2))/(Q_(1))=(W)/(Q_(1))`

`W=e(Q_(1))=(0.5947)(100)=59.47MJ`

Hence the of heat transferred to the river Is
`Q_(2) -W = (100 -59.47=40.53`