Question

If R is a gas constant and CP and CV are specific heats for a solid per mole, then for the solid -

• A.
• B. < R
• C.
• D. is negative

Answer 1

The correct option is B < R

$Forasolid$ $C_P={\left|\frac{\delta Q}{\delta T}\right|}_P={\left|\frac{\delta U}{\delta T}\right|}_P+{\left|\frac{\delta W}{\delta T}\right|}_P={\left|\frac{\delta U}{\delta T}\right|}_P+{\left|\frac{P\delta U}{\delta T}\right|}_P={\left|\frac{P\delta U}{\delta T}\right|}_P{C}_V={\left|\frac{\delta Q}{\delta T}\right|}_V={\left|\frac{\delta U}{\delta T}\right|}_V+{\left|\frac{P\delta U}{\delta T}\right|}_v=\frac{dU}{dT}+0$
$C_p$> $C_v,{\left(\frac{P\delta V}{\delta T}\right)}_{P}forasolidislessthan{\left(\frac{P\delta V}{\delta T}\right)}_P=Rforagas$
$\therefore C_p-C_V$ < $R$