38 Problem El Sdutiom on Thermodpmica El Statiatical Mechanics
Solution:
When M is burned in the power plant, the work it provides is
= 76.2J.
This is delivered in the form of electric energy.
(a) When it is delivered to residential resistance-heating radiators, it(b) When the electricity is delivered to a residential heat pump, heat
flows from a source of lower temperature to a system at higher temperature,
the working efficiency being
will transform completely into heat: Q' = W = 76.2J.
m
&=- '' = 273/30 = 9.1
Tl - T2
Hence the heat provided for the house is
Q' = (1 + E)W = 770 J.1043
An air conditioner is a device used to cool the inside of a home. It is, in
essence, a refrigerator in which mechanical work 4 done and heat removed
from the (cooler) inside and rejected to the (warmer) outside.
A home air conditioner operating on a reversible Carnot cycle between
the inside, absolute temperature T2, and the outside, absolute tempera-
ture TI > T2, consumes P joules/sec from the power lines when operating
continuously.
(a) In one second, the air conditioner absorbs 92 joules from the house
and rejects Q1 joules outdoors. Develop a formula for the efficiency ratio
Q2/P in terms of TI and T2.
(b) Heat leakage into the house follows Newton's law Q = A(T1 - T2).
Develop a formula for T2 in terms of TI, P, and A for continuous operation
of the air conditioner under constant outside temperature TI and uniform
(in space) inside temperature T2.
(c) The air conditioner is controlled by the usual on-off thermostat
and it is observed that when the thermostat set at 2OoC and an outside