(a) If TH=600 K and Tc = 400 K, what is the thermal efficiency? (b) If TH=500°C, Tc = 20°C, and Wcycle = 200 kJ, what are QH and Qc, each in kJ? (c) If n = 50% and Tc = 40°F, what is TH, in °F?
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- Check Your Understanding A Carnot engine operates between reservoirs at 400 and 30 . (a) What is the efficiency of the engine? (b) If the engine does 5.0 J of work per cycle, how much heat per cycle does it absorb from the high-temperature reservoir? (c) How much heat per cycle does it exhaust to the cold-temperature reservoir? (d) What temperatures at the cold reservoir would give the minimum and maximum efficiency?A Carnot engine operates between 550 and 20 baths and produces 300 kJ of energy in each cycle. Find the change in entropy of the (a) hot bath and (b) cold bath, in each Carnot cycle?Check Your Understanding A quantity of heat Q is absorbed from a reservoir at a temperature Th by a cooler reservoir at a temperature Tc . What is the entropy change of the hot reservoir, the cold reservoir, and the universe?
- An engine is found to have an efficiency of 0.40. If it does 200 J of work per cycle, what are the corresponding quantities of heat absorbed and discharged?A diatomic ideal gas is brought from an initial equilibrium state at p1=0.50 atm and T1=300K to a final stage with p2=0.20 atm and T1=500K. Use the results of the previous problem to determine the entropy change per mole of the gas.Is it possible for the efficiency of a reversible engine to greater than 1.0? Is it possible for the coefficient of performance of a reversible refrigerator to be less than 1.0?
- A Carnot cycle working between 100 and 30 is used to drive a refrigerator between 10 and 30 . How much energy must the Carnot engine produce per second so that the refrigerator is able to discard 10 J of energy per second?If a refrigerator discards 80 J of heat per cycle and its coefficient of performance is 6.0, what are (a) the quantity off heat it removes per cycle from a cold reservoir and (b) the amount of work per cycle required for its operation?The gasoline internal combustion engine operates in a cycle consisting of six parts. Four of these parts involve, among other things, friction, heat exchange through finite temperature differences, and accelerations of the piston; it is irreversible. Nevertheless, it is represented by the ideal reversible Otto cycle, which is illustrated below. The working substance of the cycle is assumed to be air. The six steps of the Otto cycle ale as follows: i. Isobaric intake stroke (OA). A mixture of gasoline and air is drawn into the combustion chamber at atmospheric pressure P0 as the piston expands, increasing the volume of the cylinder from zero to VA . ii. Adiabatic compression stroke (AB). The temperature of the mixture rises as the piston compresses it adiabatically from a volume VA to VB . iii. Ignition at constant volume (BC). The mixture is ignited by a spark. The combustion happens so fast that there is essentially no motion of the piston. During this process, the added heat Q1 causes the pressure to increase from pB to pc at the constant volume VB(=Vc) . iv. Adiabatic expansion (CD). The heated mixture of gasoline and air expands against the piston, increasing the volume from VC to VD . This is called the power stroke, as it is the part of the cycle that delivers most of the power to the crankshaft. v. Constant-volume exhaust (DA). When the exhaust valve opens, some of the combustion products escape. There is almost no movement of the piston during this part of the cycle, so the volume remains constant at VA(=VD) . Most of the available energy is lost here, as represented by the heat exhaust Q2 . vi. Isobaric compression (AO). The exhaust valve remains open, and the compression from VA to zero drives out the remaining combustion products. (a). Using (i)e=W/Q1; (ii)w=Q1Q2; and (iii)Q1=nCv(TCTB),Q2=nCv(TDTA), Show that e=1TDTATCTB. (b). Use the fact that steps (ii) and (iv) are adiabatic to show that e=11r1 where r=VA/VB . The quantity r is called the compression ratio of the engine. (c) In practice, r is kept less than around 7. For larger values, the gasoline-air mixture is compressed to temperatures so high that it explodes before the finely timed spark is delivered. This preignition causes engine knock and loss of power. Show that for r=6 and =1.4 (the value for air), e=0.51 , or an efficiency of 51%. Because of the many irreversible processes, an actual internal combustion engine has an efficiency much less than this ideal value. A typical efficiency for a tuned engine is about 25% to 30%.
- Check Your Understanding A Carnot refrigerator operates between two heat reservoirs whose temperatures 0 and 25 . (a) What is the coefficient of performance of the refrigerator? (b) If 200 J of work done on the working substance cycle, how heat per cycle is from cold reservoir? (c) How much heat cycle is discarded to the hot reservoir?Two hundred joules of heat are removed from a heat at a temperature of 200 K. What is the entropy change of the reservoir?A refrigerator has a coefficient of performance of 3.0. (a) If it requires 200 J of work per cycle, how much heat per cycle does it remove the cold reservoir? (b) How much cycle is discarded to the hot reservoir?