A homeowner is trying to decide between a highefficiency natural gas furnace with an efficiency of 97 percent and a ground-source heat pump with a COP of 3.5. The unit costs of electricity and natural gas are $0.115/kWh and $1.42/therm (1 therm = 105,500 kJ). Determine which system will have a lower energy cost.

Suppose a heat engine is connected to two energy reservoirs, one a pool of molten aluminum (660°C) and the other a block of solid mercury (-38.9°C). The engine runs by freezing 1.40 g of aluminum and melting 16.0 g of mercury during each cycle. The heat of fusion of aluminum is 3.97 x 105 J/kg; the heat of fusion of mercury is 1.18 x 104 J/kg. What is the efficiency of this engine? 74.9 4 X Note that the usable energy in a heat engine is the difference between the energy input and the exhaust energy. % Need Help? Watch It Additional Materials eBook

A heat engine takes 1800 kcal of heat from a hot reservoir at 270oC and vents 1200 kcal to a cold reservoir at 40oC. What is the efficiency of this heat engine and what is the maximum efficiency that any heat engine between these two reservoirs could have?

4. Suppose that a nuclear power plant has an efficiency of about 0.34, and generates 1000 MW of power. It is located on the banks of a major river that is 67 m wide near the plant, approximately 3 m deep, and flows at a rate of 0.5 m/s. Suppose that the plant re-routes all of this water into the plant and dumps its waste heat evenly throughout the water, then returns the warmer water to the river. How much warmer is the river downstream of the plant compared to upstream? Water's specific heat is approximately 4184 J/kg/K, and its density is 1000 kg/m³. [Answer: The water is warmer by 4.62 K. This is a lot warmer!]

A particular power plant operates with a heat-source reservoir at 350°C and a heatsink reservoir at 30°C. It has a thermal efficiency equal to 55% of the Carnot-engine thermal efficiency for the same temperatures. What is the thermal efficiency of the plant? To what temperature must the heat-source reservoir be raised to increase the thermal efficiency of the plant to 35%? Again, η is 55% of the Carnot-engine value

Problem 2:   This problem compares the energy output and heat transfer to the environment by two different types of nuclear power stations—one with the normal efficiency of 36 %, and another with an improved efficiency of 47 %. Suppose both have the same heat transfer into the engine in one day, 2.5 × 1014 J  Part (a)  How much more electrical energy is produced by the more efficient power station?  Part (b)  What is the change in the heat transfer to the environment after the upgrade to the more efficient power station?

Question 6. in one cycle, a heat engine does 700J of work and releases 1450 J of heat to a lower-temperature reservoir. What is the efficiency of this engine, in percent?

A power plant uses natural gas energy to heat up steam. The steam at 400 deg C generates electric power, then is condensed, and the water is cooled to 30 deg C. The cycle repeats. The maximum possible efficiency of electricity generation is %.