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### Thermodynamics Nomenclature:

T = temperature (^{o}K) |

V = volume of system (cubic metres) |

P or p = pressure at the boundary of the system and its environment, (in pascals) |

W = work done by or on a system (joules) |

Q = heat transfer in or out of a system (joules) |

q = specific heat transfer in or out of a system (joules per kg) |

U = internal energy of a system mainly contained in solid and liquid components (joules) |

u = specific internal energy of a system (joules per kg) |

H = enthalpy of a system (joules) |

h = specific enthalpy (joules per kg) |

S = entropy (joules per ^{o}K) |

s = specific entropy (joules per kg per ^{o}K) |

n = heat capacity ratio (= C_{v}/C_{p}) |

### Thermodynamics Equations:

Thermodynamics equations can be difficult to understand. The following is a simpified summary where the term "system" can be equated to a steam locomotive's cylinder:

**The First Law of Thermodynamics **(conservation of energy) can be expressed as "*The increase in internal energy of a system* = the *heat supplied to the system minus the energy that flows out in the form of Work that the system performs on it environment*" [ref Wikipedia]. In this case, the external "environment" is the locomotive's piston, hence the definition can be formulated by the equation:

**δU = Q - W**_{piston} ............ (1)

which may also be written: ** **

**dU = dQ - dW**_{piston} .......... (1a)

However, the work done on a system (locomotive cylinder) by changing its volume is **dW = p.dV**, hence:

**dU = dQ - p.dV **............. (1b)

If the process (steam expansion) is assumed to be **adiabatic** - i.e. with no heat transfer in or out, then **dQ = 0**, whence

**dU = - p.dV **................... (1c)

However** Enthalpy** (see separate page) is defined as the sum of a system's internal energy plus the product of its pressure and volume - i.e.

**H = U + P.V** .................(2)

from which a change in enthalpy can be defined (by differentiation) as

**dH = dU + p.dV + V.dp **.................(2a)

Thus by combining equations (1c) and (2a) we get (**for adiabatic expansion**): dH = -p.dV + p.dV + V.dp, or

**dH = V.dp** .................(3)

Combining eqns (1c) and (3) gives:

**dH/dU = - V.dP / P.dV** ................. (4)

**The Second Law of Thermodynamics **(heat always flows to regions of lower temperature) can be expressed as "*a change in the entropy (**S) of a system is the infinitesimal transfer of heat (**Q) to a closed system driving a reversible process, divided by the equilibrium temperature (**T) of the system*" [ref Wikipedia]. This definition is formulated by the equation:^{}

**dS = δQ/T** or **dQ = T.dS** ..................(5)

** **

By combining Eqn (4) with (1b), a change in internal energy is given by:

**dU = T.dS - p.dV** ...............................(6)

**Ideal Gas Laws** (from physics): The ideal gas law is defined by the equation:

**pV ^{n} = k** ............................... (7)

where n is the "heat capacity ratio": **n = C _{p} / C_{v} = - V.dp / p.dV** [ref Wikipedia]

Thus from equation (4): **n = ****dH/dU **

------------------------ page in progress as at 10th Mar 2011 ** ------------------**