Question

Question 4 | A heat engine utilizes a heat source at 550°C and has an ideal (Carnot) cfficiency of28%. T o increase the ideal efficiency to 35%, what must be the temperature of the heat source?

Answer 1

The efficiency at 550^oC is

where Tc is the temperature of heat source in Kelvin

Therefore

$\frac{T_c}{T_h}=1-0.28=0.72$ ....(1)

When the efficiency is 35 %

$\frac{T_c}{T_h'}=1-0.35=0.65$ .......(2)

Dividing (1) by (2)

$\frac{T_h'}{T_h}=\frac{0.72}{0.65}=1.11$

Therefore the new temperature of the heat source has to be

$T_h'=1.11T_c=1.11\times (550+273.15)=911.8\,\,K$

In celsius the temperature is

$T_c'=911.8-273.15=638.65\,\,^oC$