written 8.3 years ago by | • modified 8.3 years ago |
Mumbai university > MECH > SEM 3 > THERMO
Marks: 4M
Year: May 2014
written 8.3 years ago by | • modified 8.3 years ago |
Mumbai university > MECH > SEM 3 > THERMO
Marks: 4M
Year: May 2014
written 8.3 years ago by | • modified 8.3 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.