Why there are cp and cv for gases but not for solids?
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The specific heats of gases are given as Cp and Cv at constant pressure and constant volume respectively while solids and liquids are having only single value for specific heat.
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Looking at the derivation of the formula
Cp-Cv=R,
delta(U) + delta(PV)=delta(H)
NCv(dt) + NR(dt)= NCp(dt)
Cp-Cv=R
Firstly and obviously we can't substitute PV=NRT in case of solids, as its true for ideal gases only. This term is mostly experimentally calculated at different temperatures and the value is in the order of 10^-3 whereas the rest two terms have the order of 10^3-10^4. That makes delta(PV) almost negligible and Cp and Cv have almost identical values.
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