Determine whether or not it is possible to compress air adia

Determine whether or not it is possible to compress air adiabatically from 70 kPa and 310 K to 140kPa and 400 K. A closed piston-cylinder assembly contains 0.5 kg of water initially at 800 kPa and 435 K. As a result of heal transfer during an internally reversible isothermal process, the water reaches a final pressure of 150 kPa. Determine the heal transfer and work, in kilojoules, for this process. Heat is added to a heat pump from a reservoir at - 10 degree C and 9 kJ/s of heat is rejected to a reservoir at 25 degree C. Determine the coefficient of performance if a power input of 4 kW is required to drive the heat pump. Compare this value with the coefficient of performance of a Carnot heat pump operating between the same two reservoirs.

Solution

Given P1 =800 KPA

P2 =150 KPa

T =435 K (constant)

Isothermal process, T constant => work done PDV+VDP, but since V constant work is VDP

from ideal gas eqn PV=nRT

n = .5/18 moles , R= 8.314 J/mol K

net work = nRT Ln(P2/P1) = .5/18 * 8.314 * 435 * ( ln 800 -ln 150) Joules ( heat equiv)

=100.46*1.674 J =168.2 J