Question

A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. In 5 minutes of operation of the engine, the heat rejected by the engine melts a mass of ice equal to 4.35×10−2 kg . Throughout this problem use Lf=3.34×105J/kg for the heat of fusion for water.

Answer 1

Step-by-step explanation:

Given

In 5 minute
`m=4.35* 10^(-2) kg` of ice is melted

Latent heat of Fusion
`L=3.34* 10^5 J/kg`

`T_1=273 K,T_2=373 K`

Heat Rejected
`Q_r=m* L=4.35* 10^(-2)* 3.34* 10^5`

`Q_r=14.529* 3 J`

`\eta _(carnot)=1-(Q_r)/(Q_s)=1-(T_1)/(T_2)`

`(Q_r)/(Q_s)=(T_1)/(T_2)`

`Q_s=Q_r* (T_2)/(T_1)`

`Q_s=14.529* (373)/(273)`

`Q_s=19.85 kJ`

`Work\ done=Q_s-Q_r`

`W=5.32\ kJ`