Question

A carnot engine has its source at 120°C and its sink is maintained at a constant temperature by means of ice at 0°C. If it is working at the rate of 175 watts, how much ice will melt in two minutes?

Answer 1

Given data

Temperature of source $(T$_source)=120⁰C+273

=393 K

Temperature of sink (T_sink)=0⁰C+273

=273 K

Working rate (power) =175 watts

Workdone by carnot engine in 2 minutes

$W=P\times t$

$W=175\times2 \times60$

$W=21000 J$

efficiency of carnot engine

$e=1-\frac{T_{sink}}{T_{source}}$

$e=1-\frac{273}{393}$

$e=\frac{120}{393}=0.305$

efficiency of carnot engine can be given by formula mention below

$e=\frac{W}{Q}$ Where Q is heat rejected at sink

therefore $Q= \frac{W}{e}$

$Q=\frac{21000}{0.305}$

$Q=6405J$

This rejected heat will melt the ice and can be given by below

$Q={m}{L_{f}}$

where m is the mass of melted ice and L_f is latent heat of fusion.

therefore

$m=\frac{Q}{L_f}$ value of latent heat of fusion for

ice L_f =$3.33\times10^5 J/Kg$

by putting the value of Q annd L_f

$m=\frac{6405}{3.33\times 10^5}$

$m=0.21328\space Kg$

$\colorbox{aqua}{m=0.21 Kg}$

therefore mass of melted ice is 0.21 Kg in 2 minutes.