Question 548: Thermodynamics & KTG

Question

A heat engine operates between a cold reservoir at temperature T
2
= 400 K and a hot reservoir at temperature T
1
. It takes 300 J of heat from the hot reservoir and delivers 240 J of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be ______________ K.

Accepted Answer

Q
in
= 300 J ; Q
out
= 240 J
Work done = Q
in
$$-$$ Q
out
= 300 $$-$$ 240 = 60 J
Efficiency = $${W \over {{Q_{in}}}} = {{60} \over {300}} = {1 \over 5}$$
efficiency = $$1 - {{{T_2}} \over {{T_1}}}$$
$${1 \over 5} = 1 - {{400} \over {{T_1}}} \Rightarrow {{400} \over {{T_1}}} = {4 \over 5}$$
T
1
= 500 k

Thermodynamics & KTG

A heat engine operates between a cold reservoir at temperature T 2 = 400 K and a hot reservoir at temperature T 1 . It takes 300 J of heat from the hot reservoir and delivers 240 J of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be ______________ K.

Integer / Numeric Answer Type