Water is heated from \(2^{\circ} \mathrm{C}\) to \(78^{\circ} \mathrm{C}\) at a constant pressure of \(100 \mathrm{kPa}\). The initial density of water is \(1000 \mathrm{~kg} / \mathrm{m}^{3}\) and the volume expansion coefficient of water is \(\beta=0.377 \times\) \(10^{-3} \mathrm{~K}^{-1}\). The final density of the water is

(a) \(28.7 \mathrm{~kg} / \mathrm{m}^{3}\)

(b) \(539 \mathrm{~kg} / \mathrm{m}^{3}\)

(c) \(997 \mathrm{~kg} / \mathrm{m}^{3}\)

(d) \(984 \mathrm{~kg} / \mathrm{m}^{3}\)

(e) \(971 \mathrm{~kg} / \mathrm{m}^{3}\)