Question

A carnot's engine is operated between two reservoirs at temperatures of 500 K and 400 K. If engine receives 2000 calories of heat from the source in each cycle then calculate (a) amount of heat rejected to sink in each cycle (b) work done by engine in each cycle in terms of joule

Answer 1

solution

given data:-

temperature of source(T₁)=500K

temperature of sink(T₂)=400K

heat received by the engine from source(Q₁)=2000Calories

[1 calori=4.184J]

then $Q_1=2000\times 4.184$

Q₁=8368J

(a) using carnot engine relation between temperatures of source and sink and heat of source and sink is given by

$\frac{T_2}{T_1}= \frac{Q_2}{Q_1}$

then heat rejected to sink can be given by

$Q_2=\frac{T_2\times Q_1}{T_1}$

by putting the value of T₁ ,T₂ and Q₁

$Q_2=\frac{400\times 8368}{500}$

$\colorbox{aqua}{$Q_2=6694.4J$}$

therefore heat rejected to sink is 6694.4J.

(b) work done by the engine in one cycle is given by

$W=Q_1-Q_2$

then

$W=8368-6694.4$

$\colorbox{aqua}{$W=1673.6J$}$

therefore work done by the engine in one cycle is 1673.6J.