Question 554: Thermodynamics & KTG

Question

For an ideal heat engine, the temperature of the source is 127$$^\circ$$C. In order to have 60% efficiency the temperature of the sink should be ___________$$^\circ$$C. (Round off to the Nearest Integer)

Accepted Answer

Given, temperature of source, T
H
= 127$$^\circ$$C
= 273 + 127 = 400 K
Efficiencies, $$\eta $$ = 60% = 0.6
The efficiency of Carnot (ideal) heat engine is given by
$$\eta  = \left( {1 - {{{T_L}} \over {{T_H}}}} ight)$$
where, T
L
= temperature of sink,
$$0.6 = \left( {1 - {{{T_L}} \over {{T_H}}}} ight) \Rightarrow {{{T_L}} \over {{T_H}}} = 1 - 0.6$$
$${{{T_L}} \over {{T_H}}} = 0.4 \Rightarrow {T_L} = 0.4 	imes {T_H}$$
$$ = 0.4 	imes 400 = 160K$$
$$ = 160 - 273 =  - 113^\circ C$$

Thermodynamics & KTG

For an ideal heat engine, the temperature of the source is 127$^\circC. In order to have 60% efficiency the temperature of the sink should be ___________^\circ$C. (Round off to the Nearest Integer)

Integer / Numeric Answer Type