Thermodynamics

292 | Thermodynamicsheat to the house at the same rate, that is, at a rate of 80,000 kJ/h. Thenthe rate of heat transfer from the outdoor becomesQ # L Q # H W # net,in 180,000 32,0002 kJ>h 48,000 kJ/hDiscussion Note that 48,000 of the 80,000 kJ/h heat delivered to thehouse is actually extracted from the cold outdoor air. Therefore, we are payingonly for the 32,000-kJ/h energy that is supplied as electrical work to theheat pump. If we were to use an electric resistance heater instead, we wouldhave to supply the entire 80,000 kJ/h to the resistance heater as electricenergy. This would mean a heating bill that is 2.5 times higher. Thisexplains the popularity of heat pumps as heating systems and why they arepreferred to simple electric resistance heaters despite their considerablyhigher initial cost.Warm environmentRQ H = 5 kJQ L = 5 kJCold refrigerated spaceW net,in = 0FIGURE 6–26A refrigerator that violates theClausius statement of the second law.The Second Law of Thermodynamics:Clausius StatementThere are two classical statements of the second law—the Kelvin–Planckstatement, which is related to heat engines and discussed in the precedingsection, and the Clausius statement, which is related to refrigerators or heatpumps. The Clausius statement is expressed as follows:It is impossible to construct a device that operates in a cycle and producesno effect other than the transfer of heat from a lower-temperature body to ahigher-temperature body.It is common knowledge that heat does not, of its own volition, transferfrom a cold medium to a warmer one. The Clausius statement does notimply that a cyclic device that transfers heat from a cold medium to awarmer one is impossible to construct. In fact, this is precisely what a commonhousehold refrigerator does. It simply states that a refrigerator cannotoperate unless its compressor is driven by an external power source, such asan electric motor (Fig. 6–26). This way, the net effect on the surroundingsinvolves the consumption of some energy in the form of work, in addition tothe transfer of heat from a colder body to a warmer one. That is, it leaves atrace in the surroundings. Therefore, a household refrigerator is in completecompliance with the Clausius statement of the second law.Both the Kelvin–Planck and the Clausius statements of the second law arenegative statements, and a negative statement cannot be proved. Like anyother physical law, the second law of thermodynamics is based on experimentalobservations. To date, no experiment has been conducted that contradictsthe second law, and this should be taken as sufficient proof of its validity.Equivalence of the Two StatementsThe Kelvin–Planck and the Clausius statements are equivalent in their consequences,and either statement can be used as the expression of the second lawof thermodynamics. Any device that violates the Kelvin–Planck statementalso violates the Clausius statement, and vice versa. This can be demonstratedas follows.