# Enthalpy and specific heat

h = u+ Pv

For an ideal gas u = u(T) only and PV
= mRT and hence h = h(T) only.

## Specific heat at constant volume

The specific heat at constant volume is defined as the
amount of energy transferred as heat at constant volume, per unit mass of a
system to raise its temperature by one degree. That is,

C_{v} = (dq/dT)_{v}

## Specific heat at constant pressure

The specific heat at constant pressure is defined as the energy transferred as heat at constant pressure, per unit mass of a substance to raise its temperature by one degree. That is

C_{p} = (dq/dT)_{P}

For a constant pressure process

dq = du + dw

= du + Pdv

= du+ Pdv +vdP

(since dP=0 for a constant pressure process)

Or dq= du+d(Pv)

= d(U+ Pv) = dh or dq=dh

C_{P} = (∂h/∂T)_{P}

The ratio of
specific heat (Î³) is given by

Î³= C _{P}/C_{v}

For mono-atomic
ideal gases Î³ = 1.67 and for diatomic gases Î³= 1.4.

_{}

ConversionConversion EmoticonEmoticon