An air-conditioning system involves the mixing of cold air and warm outdoor air before the mixture is routed to the conditioned room in steady operation. Cold air enters the mixing chamber at $5^{\circ} \mathrm{C}$ and $105 \mathrm{~kPa}$ at a rate of $1.25 \mathrm{~m}^{3} / \mathrm{s}$ while warm air enters at $34^{\circ} \mathrm{C}$ and $105 \mathrm{~kPa}$. The air leaves the room at $24^{\circ} \mathrm{C}$. The ratio of the mass flow rates of the hot to cold air streams is $1.6$. Using variable specific heats, determine $(a)$ the mixture temperature at the inlet of the room and $(b)$ the rate of heat gain of the room.

A heat pump has a COP of 1.7. Determine the heat transferred to and from this heat pump when 50 kJ of work is supplied.

A mechanic claims to have developed a car engine that runs on water instead of gasoline. What is your response to this claim?

A $600-\mathrm{~MW}$ steam power plant, which is cooled by a nearby river, has a thermal efficiency of $40$ percent. Find the rate of heat transfer to the river water. Will the actual heat transfer rate be higher or lower than this value? Why?

A 600-MW steam power plant, which is cooled by a nearby river, has a thermal efficiency of 40 percent. Determine the rate of heat transfer to the river water. Will the actual heat transfer rate be higher or lower than this value? Why?

A commercial refrigerator with refrigerant-134a as the working fluid is used to keep the refrigerated space at $-35^\circ C$ by rejecting waste heat to cooling water that enters the condenser at $18^\circ C$ at a rate of 0.25 kg/s and leaves at $26^\circ C.$ The refrigerant enters the condenser at 1.2 MPa and $50^\circ C$ and leaves at the same pressure subcooled by $5^\circ C.$ If the compressor consumes 3.3 kW of power, determine (a) the mass flow rate of the refrigerant, (b) the refrigeration load, (c) the COP, and (d) the minimum power input to the compressor for the same refrigeration load.

A steam power plant receives heat from a furnace at a rate of 280 GJ/h. Heat losses to the surrounding air from the steam as it passes through the pipes and other components are estimated to be about 8 GJ/h. If the waste heat is trans ferred to the cooling water at a rate of 145 GJ/h, determine (a) net power output and (b) the thermal efficiency of this power plant.

When a man returns to his well-sealed house on a summer day, he finds that the house is at 35$^\circ{}$C. He turns on the air conditioner, which cools the entire house to 20$^\circ{}$C in 30 min. If the COP of the air-conditioning system is 2.8, determine the power drawn by the air conditioner. Assume the entire mass within the house is equivalent to 800 kg of air for which $c_{v}$ = 0.72 kJ/kgK and $c_{p}$ = 1.0 kJ/kgK

A household refrigerator runs one-fourth of the time and removes heat from the food compartment at an average rate of 800 kJ/h. If the COP of the refrigerator is 2.2, determine the power the refrigerator draws when running.

When a man returns to his well-sealed house on a summer day, he finds that the house is at $32^{\circ} \mathrm{C}$. He turns on the air conditioner, which cools the entire house to $20^{\circ} \mathrm{C}$ in $15 \mathrm{~min}$. If the $\mathrm{COP}$ of the air-conditioning system is $2.5$, Find the power drawn by the air conditioner. Assume the entire mass within the house is equivalent to $800 \mathrm{~kg}$ of air for which $c_{v}=0.72 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$ and $c_{p}=1.0 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$.

Show that the Kelvin-Planck and the Clausius expressions of the second law are equivalent.

Show that the Kelvin–Planck and the Clausius expressions of the second law are equivalent.

Show that the Kelvin-Planck and the Clausius expressions of the second law are equivalent.

Show that the Kelvin–Planck and the Clausius expressions of the second law are equivalent.