Question

When water is heated from $0^{\circ }C$ to $4^{\circ }C$ and $C_p$ and $C_v$ are its specific heated at constant pressure and constant volume respectively, then:

• A. $C_p>C_v$
• B. $C_p<C_v$
• C. $C_p=C_v$
• D. $C_p-C_v=R$

Answer 1

Answer: (B)

$C_p<C_v$

Water has highest density at $4^{\circ }C$. This changes its properties from other simple fluids.

When water is heated from $0^{\circ }C$ to $4^{\circ }C$, the volume of liquid decreases.

Thus for this transition, $P\Delta V$ is negative.

$\int C_{P}dT=\int C_{V}dT+P\Delta V$

$⟹C_P<C_V$