Carnot's Principle and the Carnot Engine

If the heat engine shown above acts "reversibly", this idealized engine is called a Carnot engine. A reversible process is one in which both the system and its environment (the rest of the universe) can be returned to exactly the states (of P, V, and T) they had before the process occurred.

In a Carnot engine the input heat QH originates from a hot reservoir at a single Kelvin temperature TH, and all rejected heat QC is returned to the cold reservoir at a single Kelvin temperature TC. The ratio of the rejected heat to the input heat can be shown to be

where the temperatures MUST be expressed in Kelvins. The efficiency of a Carnot engine can be written,
This relation gives the maximum possible efficiency for a heat engine operating between two Kelvin temperatures.

Adiabatic process

This article covers adiabatic processes in thermodynamics. For adiabatic processes in quantum mechanics, see adiabatic process (quantum mechanics).
In thermodynamics, an adiabatic process is a process in which no heat is gained or lost in the working fluid. For example, there are no chemical process es taking place in the fluid and there is no heat transfer from the environment. The term "adiabatic" describes things that are impermeable to heat transfer; for example, an adiabatic boundary is a boundary that is impermeable to heat transfer. An insulated wall approximates an adiabatic boundary. Another example is the adiabatic flame temperature, which is the temperature that would be achieved by a flame in the absence of heat loss to the surroundings. An adiabatic process which is also reversible is called an isentropic process.
The opposite extreme, in which the maximum heat transfer with its surroundings occurs, causing the temperature to remain constant, is known as an isothermal process.
Adiabatic heating and cooling are processes that commonly occur due to a change in the pressure of a gas. This can be quantified using the ideal gas law.
There are three rates of adiabatic cooling for air.
The ambient atmosphere lapse rate, which is the rate that air cools as one goes up in altitude.
The dry adiabatic lapse rate, -10°C per 1000m rise.
The wet adiabatic lapse rate, about -6° per 1000m rise.

The first rate is used to describe the temperature of the surrounding air that the rising air is passing through, and the second and third rates are in reference to a parcel of air that is rising through the atmosphere. The dry adiabatic lapse rate applies to air which is below its dew point, ie which is not saturated by water vapor, whereas the wet adiabatic lapse rate applies to air which has reached its dew point. Adiabatic cooling is a common cause of cloud formation.

Adiabatic cooling does not have to involve a fluid. One technique used to reach very low temperatures (thousandths and even millionths of a degree above absolute zero) is adiabatic demagnetisation , where the change in magnetic field on a magnetic material is used to provide adiabatic cooling.

Isochoric process

An isochoric process, also called an isometric process, is a thermodynamic process in which the volume stays constant; ΔV = 0. This implies that the process does no pressure-volume work, since such work is defined by

ΔW = PΔV,

where P is pressure (no minus sign; this is work done by the system).
By applying the first law of thermodynamics, we can deduce that
Q = ΔE

for an isochoric process: all the heat being transferred to the system is added to the system's internal energy. If the quantity of gas stays constant, then this increase in energy is proportional to an increase in temperature,
Q = nC_VΔT

where C_V is molar specific heat for constant volume.
On a P-V diagram, an isochoric process appears as a straight vertical line.

Isobaric process

Isobaric - the pressure is kept constant. An example of an isobaric system is a gas, being slowly heated or cooled, confined by a piston in a cylinder. The work done by the system in an isobaric process is simply the pressure multiplied by the change in volume.

Isothermal process

An isothermal process is a thermodynamic process in which the temperature of the system stays constant; ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and the system changes slowly enough to allow it to adjust to the temperature of the reservoir. The opposite extreme in which a system exchanges no heat with its surroundings is known as an adiabatic process.

Assuming that the quantity n₀ of moles of gas of the system remains constant, then the internal energy E of the system also remains constant:

ΔE = n₀RΔT = 0,

but this means, according to the ideal gas law, that

Δ(PV) = 0

so that

P_iV_i = PV = P_fV_f

where P_i is the pressure of the initial state, V_i is the volume of the initial state, P_f is the pressure of the final state, V_f is the volume of the final state, and P and V are the pressure and volume of an intermediate state of the isothermal process.

An isothermal process is shown as a hyperbolic line (T₀ = constant) on a P-V (Pressure-Volume) diagram which asymptotically approaches both the V (abcissa) axis and the P (ordinate) axis. For an ideal gas, the line is called an isotherm and its equation is



According to the first law of thermodynamics, the isotherm can be described also by the equation

Q = W

where W is work done by the system. This means that, during an isothermal process, all heat accepted by the system from its surroundings must have its energy entirely converted to work which it then performs on the surroundings, so that all the energy which comes into the system then comes right back out of the system so the internal energy (and thus the temperature) of the system remains constant.