Question

A particular heat engine has a mechanical power output of 5.00 kW and an efficiency of 25.0%. The engine expels 8.00 3 103 J of exhaust energy in each cycle. Find (a) the energy taken in during each cycle and (b) the time interval for each cycle.

Answer 1

Answer:

Explanation:

Given

Power output $P=5\ kW$

efficiency $\eta =25\ \%$

Engine expels $Q_r=8\times 10^3\ J$

Efficiency is given by

$\eta =1-\dfrac{Q_r}{Q_s}$

where $Q_s$=Heat supplied

$0.25=1-\dfrac{8\times 10^3}{Q_s}$

$0.75=\dfrac{8\times 10^3}{Q_s}$

$Q_s=\dfrac{8\times 10^3}{0.75}$

$Q_s=10.667\ kJ$

Work Produced by  cycle

$W=Q_s-Q_r$

$W=10.667-8$

$W=2.667\ kJ$

Time interval for which power is supplied

$P\times t=W$

$t=\dfrac{W}{P}$

$t=\dfrac{2.667}{5}$

$t=0.5334\ s$