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 3.30×10−2 kg . Throughout this problem use Lf=3.34×105J/kg for the heat of fusion for water.A) During this time, how much work W is performed by the engine?

Answer 1

Answer:

$W=4037.36\ J$

Explanation:

Given:

mass of ice melted, $m=3.3\times10^{-2}\ kg$

time taken by the ice to melt, $t=5\ min=300\ s$

latent heat of the ice, $L=3.34\times 10^5\ J$

Now the heat rejected by the Carnot engine:

$Q_R=m.L$

$Q_R=0.033\times 3.34\times 10^5$

$Q_R=11022\ J$

Since we have boiling water as hot reservoir so:

$T_H=373\ K$

The cold reservoir is ice, so:

$T_L=273\ K$

Now the efficiency:

$\eta=1-\frac{T_L}{T_H}$

$\eta=1-\frac{273}{373}$

$\eta=26.81\%$

Now form the law of energy conservation:

Heat supplied:

$Q_S-W=Q_R$

where:

$Q_S=$ heat supplied to the engine

$Q_S-\eta\times Q_S=Q_R$

$Q_S(1-\eta)=Q_R$

$Q_S=\frac{11022}{1-0.2681}$

$Q_S=15059.36\ J$

Now the work done:

$W=Q_S-Q_R$

$W=15059.36-11022$

$W=4037.36\ J$