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How-To:

The diagram at left depicts the Pressure-Volume diagram of a heat engine. A heat engine is a mechanism in which heat energy from a hot reservoir is tranfered to an ideal gas, which then, through a series of ideal gas processes, converts part of that energy into mechanical work and releases the rest back as thermal energy into a cold reservoir. All ideal gas processes follow the equations:

PV = nRT, and ΔEsys = Qon sys + Won sys = 1.5nRΔT, where R is the ideal gas constant (8.31), n is the moles of ideal gas, and T is the temperature of the system. The efficiency of a heat engine what percentage of the heat added to the gas is converted to mechanical energy. (N = -Wtotal/Qtotal)

To compute the engine's efficiency, find the work and heat transferred at each step, then sum these numbers over all steps and take the quotient.

The heat engine shown at left starts in the lower right and moves clockwise, and consists of any of the following ideal gas processes:

Process Constant Quantity Qsurr on sys (J) Wsurr on sys (J) ΔE (J)
Adiabatic P*Vγ (γ=1.67) 0 1.5nRΔT 1.5nRΔT
Isothemal T nRT*ln(Vf/Vi) -nRT*ln(Vf/Vi) 0
Isobaric P 2.5nRΔT -nRΔT 1.5nRΔT
Isochoric V 1.5nRΔT 0 1.5nRΔT