A possible ideal-gas cycle operates as follows: (i) from an initial state (p1, V1) the gas is cooled at constant pressure to (p1, V2); (ii) the gas is heated at constant volume to (p2, V2); (iii) the gas expands adiabatically back to (p_1, V_1). Assuming constant heat capacities, show that the thermal efficiency is 1 - gamma (V_1/V_2) - 1/(p_2/p_1) - 1 (You may quote the fact that in an adiabatic change of an ideal gas, pV^gamma stays constant, where gamma = c_p/c_v.)

15.3 cos 65 degrees trig

so here is the information for current research:

-nrel's geothermal analysts, scientists, and engineers perform a full range of research from developing advanced methods of locating and accessing geothermal resources to exploring innovative technologies to extract and produce clean energy from the heat of the earth

and here is the information for the technology of geothermal energy:

-it's clean and sustainable

-resources of geothermal energy range from the shallow ground to hot water and hot rock found a few miles beneath the earth's surface, and down even deeper to the extremely high temperatures of molten rock called magma

-almost everywhere, the shallow ground or upper 10 feet of the earth's surface maintains a nearly constant temperature between 50° and 60°f (10° and 16°c)

-geothermal heat pumps can tap into this resource to heat and cool buildings

-a geothermal heat pump system consists of a heat pump, an air delivery system (ductwork), and a heat exchanger-a system of pipes buried in the shallow ground near the building

-in the winter, the heat pump removes heat from the heat exchanger and pumps it into the indoor air delivery system

-in the summer, the process is reversed, and the heat pump moves heat from the indoor air into the heat exchanger

-the heat removed from the indoor air during the summer can also be used to provide a free source of hot water