A one-dimensional chain consists of a set of N rods each of length a. When stretched by a load, each rod can align either parallel or perpendicular to the length of the chain. The energy of a rod is -ɛ when perpendicular to it. When the chain is in thermal equilibrium at temperature T, its average length is
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- 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.A certain coal-fired power plant has a rated power capacity of P = 850 MW. The output of this plant is W = 0.26QH, where QH is the energy input as heat from the hot reservoir. a. If the power plant operates for a full day at its rated capacity, how much energy QH in MJ is needed? b. If, on average, one ton of coal contains Q = 25 GJ of energy, how many tons nH of coal would the plant need to operate for a day at its rated capacity? c. How many tons nC of this coal is exhausted as wasted heat to QC in a single day?A simple pendulum is suspended from the ceiling by means of a string and this time, the pendulum is 2.40 m long and has a mass of 3.23 kg. You give it a push away from vertical so that it starts swinging with a speed of 2.93 m/s. Due to friction at the pivot point, 1.00 Joule of the pendulum s initial kinetic energy is lost as heat during the upward swing. What maximum angle will it reach, with respect to the vertical, before falling back down? 39.5 degrees 33.8 degrees 35.1 degrees 43.9 degrees
- Energy as heat is input into a steam turbine to convert 13.0 kg of liquid water at 25.0°C to water vapor at 100.0°C every hour. The efficiency of this heat engine is 21.8%. (A) What is the power output of the heat engine, in watts? (B) The temperature of the heat engine's boiler is 100.0°C, while the exhaust reservoir is maintained at 8.00°C. What is the difference between the theoretical maximum efficiency if the engine, and its actual efficiency? Please express your answer as a percentage.An ideal heat engine operates between 177 degree C and 27 degree C. If the engine takes 5*1000000 J of heat from the source, how much work does it perform?a rock with mass0.15kg is placeedin a sling shot and the elastic band of the sling shot is stretched by 70 cm from its relaxed position to store elastic potential energy in it. the spring constant of the elastic band is 28,5 N . the elastic band is then released to launched the rock. what is the speed of the rock when it leaves the sling shot if a) no heat is produced when the Celtic band is released? b: 2.8 J of heat energy are produced when the elastic band is released?
- A Carnot heat engine receives 700kJ/s from a heat source and produces 430 kW of power. At what rate is heat transferred? What is the thermal efficiency of this heat engine?You are hired to build a geothermal power plant that absorbs heat from a hot water spring and discards heat into the surrounding air, which is at a temperature of 17°. The plant is designed for a maximum (Carnot) efficiency of 0.21. What is the temperature, in degrees Celsius, of the hot water gushing from the spring? If the rate of energy supplied to the plant by the hot-water source is 4.6 kW, what is the plant’s maximum rate of power output, in kilowatts?The metabolic power for typing is 150 W for bob. For how long would bob have to type to use all the energy available in a typical fast food meal of burger, fries, and a drink, which the meal energy content is 5660 kJ (1350 food calorie), in hours?
- In a process of an ideal gas, the pressure is halved while the volume is kept constant. During this process, 750J of heat flows out of gas. What is the change in the internal energy of the gas in this process?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 eBookThe power output of a car engine running at 2300 rpmrpm is 300 kW . (a) How much work is done per cycle if the engine's thermal efficiency is 40.0 %?Give your answer in kJ. Win =7.83kJ (b)How much heat is exhausted per cycle if the engine's thermal efficiency is 40.0 %?Give your answer in kJ.