Density of water at $4^\circ\text{C}$ and $20^\circ\text{C}$ are $1000\ \text{kg/m}^3$ and $998\ \text{kg/m}^3$ respectively. The increase in internal energy of 4 kg of water when it is heated from $4^\circ\text{C}$ to $20^\circ\text{C}$ is ______ J.
(specific heat capacity of water $= 4.2\ \text{J/kg}$. and 1 atmospheric pressure $= 10^5\ \text{Pa}$ )
Answer: (A) 268799.2
(The specific heat of water is $4.2$ kJ/kg·°C $= 4200$ J/kg·°C; the unit in the statement is a misprint.)
Heat supplied: $Q = mc\Delta T = 4\times4200\times16 = 268800$ J.
Work done by the water as it expands against atmospheric pressure:
$$W = P\Delta V = 10^5\left(\frac4{998} - \frac4{1000}\right) = 10^5\times\frac{4\times2}{998000} \approx 0.80\ \text{J}$$
$$\Delta U = Q - W = 268800 - 0.8 = 268799.2\ \text{J}$$
Solution by Sreeraj P, M.Sc Physics