# Carnot cycle

The Carnot cycle is the most important closed loop process in thermodynamics. We illustrate it here for an ideal gas. This is a four step loop process as illustrated in Figure 4.3. The branch ab is along a hot isotherm at temperature Th during which heat Qh is transferred to the system from the hot reservoir. The next step is an adiabatic expansion bc to the cooler temperature Tc. The third step, cd is isothermal and an amount of heat Qc(> 0) is expelled from the system to the cooler reservoir at Tc. Finally, there is the adiabatic compression da, which completes the cycle a p(hPa) 1750 1500 1250 1000 750 500 250

a p(hPa) 1750 1500 1250 1000 750 500 250 Isotherm Tc

Isotherm Tc y(m3)

Figure 4.3 Carnot cycle for 1 kg of dry air (taken as an ideal gas) in the V-p plane. The cycle proceeds as follows. Step ab is an isothermal expansion from a to b, at temperature Th, drawing in heat Qh. Step bc is an adiabatic expansion from b to c. Step cd is an isothermal compression at temperature Tc expelling heat Qc from the system. Finally, step da is an adiabatic compression from d to a. In this case Va = 0.50m3, T2 = 300K, Vb = 1.50m3, Ti = 200K. Then all other intersections are determined, e.g., pa =1720hPa, pb = 574hPa.

back to the starting point a. We can list the products:

Wbc(> 0), Wbc = -AbcU = Mcv(Th - Tc) Wcd(< 0), Wcd = MRTc ln = -Qc(< 0) Wda (< 0), Wda = -AdaU = Mcv (Tc - Th)