Carnot Cycle

Introduction

1. Isothermal expansion: Heat is transferred from the hot reservoir to the gas.
2. Isentropic (reversible adiabatic) expansion: without transfer of heat to or from a system, so that Q = 0, is called adiabatic, and such a system is said to be adiabatically isolated. Eg. the compression of a gas within a cylinder of an engine is assumed to be rapid that little of the system's energy is transferred out as heat to the surroundings.
3. Isothermal compression
4. Isentropic compression

Ideal Gas

$pV=nRT$, or more genrally polytropic process: $pV^{\gamma }=C$, where

1. n = 0: isobaric
2. n = ∞: isochoric
3. n = 1: isothermal
4. n = γ: isentropic

Adiabatic index $\gamma =c_{p}/c_{v}$ is for the air 7/5. For the ideal gas we have $p^{1-\gamma }T^{\gamma }=C$ and $TV^{\gamma -1}=C$.

1. (n=1) Isothermal compression: T is constant, thus we have $p=C/V$.
2. (n=γ) Isentropic $p=C/V^{\gamma }$