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Mumbai university > MECH > SEM 3 > THERMO

**Marks:** 4M

**Year:** May 2014

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Derive Maxwell's equations.

written 7.7 years ago by | • modified 7.7 years ago |

Mumbai university > MECH > SEM 3 > THERMO

**Marks:** 4M

**Year:** May 2014

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written 7.7 years ago by | • modified 7.7 years ago |

A pure substance existing in a single phase has only two independent variables.

Of the eight quantities p, V, T, S, U, H, F (Helmholtz function), and G (Gibbs function) any one may be expressed as a function of any two others.

For a pure substance undergoing an infinitesimal reversible process

a) dU = TdS - pdV

b) dH = dU + pdV + Vdp = TdS + Vdp

c) dF = dU - TdS - SdT = -pdV - SdT

d) dG = dH - TdS - SdT = Vdp - SdT

Since U, H, F and G are thermodynamic properties and exact differentials of the type $$dz = Mdx + Ndy$$ then

$(\frac{∂M}{∂y})_x = (\frac{∂N}{∂x})_y$

Applying this to the four equations we get,

$(\frac{dT}{dv})_s = (\frac{∂P}{∂s})_v$

$(\frac{dT}{dP})_s = (\frac{∂v}{∂s})_P$

$(\frac{∂s}{∂v})_T = (\frac{∂P}{∂T})_v$

$(\frac{∂s}{∂P})_T = (\frac{∂v}{∂T})_P$

These four equations are known as Maxwell’s equations.

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