5.13 Before introducing the temperature scale now known as the

5.13 Before introducing the temperature scale now known as the Kelvin scale Kelvin suggested a
logarithmic scale in which the function ψ of Eq. 5.5 takes the form
where θH and θC denote, respectively, the temperatures of the hot and cold reservoirs on this scale.
(a) Show that the relation between the Kelvin temperature T and the temperature θon the
logarithmic scale is
where C is a constant.
(b) On the Kelvin scale, temperatures vary from 0 to +∞. Determine the range of temperature values
on the logarithmic scale.
(c) Obtain an expression for the thermal efficiency of any system undergoing a reversible power
cycle while operating between reservoirs at temperatures θH and θC on the logarithmic scale.
5.35 The refrigerator shown in Fig. P5.35 operates at steady state with a coefficient of performance
of 4.5 and a power input of 0.8 kW. Energy is rejected from the refrigerator to the surroundings at
20oC by heat transfer from metal coils whose average surface temperature is 28oC. Determine
(a) the rate energy is rejected, in kW.
(b) the lowest theoretical temperature inside the refrigerator, in K.
(c) the maximum theoretical power, in kW, that could be developed by a power cycle operating
between the coils and the surroundings. Would you recommend making use of this opportunity for
developing power?
5.38 At steady state, a refrigeration cycle removes 18,000 kJ/h of energy by heat transfer from a
space maintained at–40oC and discharges energy by heat transfer to surroundings at 20oC. If the
coefficient of performance of the cycle is 25 percent of that of a reversible refrigeration cycle
operating between thermal reservoirs at these two temperatures, determine the power input to the
cycle, in kW.
5.45 By supplying energy to a dwelling at a rate of 25,000 kJ/h, a heat pump maintains the
temperature of the dwelling at 20oC when the outside air is at–10oC. If electricity costs 8 cents per
determine the minimum theoretical operating cost for each day of operation.