Density of water at 4 ^ C and 20^ C are 1000 ~kg / m ³ and 998 ~kg / m ³ respectively. The increase in internal energy of 4 kg of water when it is heated from 4 ^ C to 20^ C is _ _ _ _ J. (specific heat capacity of water =4.2 ~J / kg . and 1 atmospheric pressure =10⁵ ~Pa )

Step-by-step solution

Heat absorbed by water: Q = mc T = 4 4200 16 = 268800 J. Volume change: V₁ = 4/1000 = 0.004 m³ at 4°C, V₂ = 4/998 ≈ 0.00401 m³ at 20°C. Work done by water at constant pressure: W = P_ atm V = 10^5 0.00001 = 0.8 J. By first law of thermodynamics: U = Q - W = 268800 - 0.8 = 268799.2 J