Density of water at 4°C and 20°C are 1000 kg/m³ and 998 kg/m³ respectively. The increase in internal energy of 4 kg water when it is heated from 4°C to 20°C i $s____J.$
(Specific heat capacity of water = 4.2 × 10³ J·kg⁻¹·°C⁻¹ and 1 atmospheric pressure = 10⁵ Pa)

Question

Density of water at 4°C and 20°C are 1000 kg/m³ and 998 kg/m³ respectively. The increase in internal energy of 4 kg water when it is heated from 4°C to 20°C i $s____J.$

(Specific heat capacity of water = 4.2 × 10³ J·kg⁻¹·°C⁻¹ and 1 atmospheric pressure = 10⁵ Pa)

G1 Physics · Accepted Answer

Heat supplied to the water is Q = mcΔT. Here, m = 4 kg, c = 4.2×10³ J·kg⁻¹·°C⁻¹, ΔT = 20-4 = 16°C. Therefore, Q = 4×4200×16 = 268800 J. At atmospheric pressure, the expansion work is W = PΔV. The initial and final volumes are Vᵢ = m/ρᵢ, V𝒇 = m/ρ𝒇. Hence, ΔV = m(1/ρ𝒇 - 1/ρᵢ) = 4(1/998 - 1/1000) m³. With P = 10⁵ Pa, W = 10⁵×4(1/998 - 1/1000) ≈ 0.8 J. From the first law, ΔU = Q-W. Thus, ΔU = 268800-0.8 = 268799.2 J. Correct option: D.

Density of water at 4°C and 20°C are 1000 kg/m³ and 998 kg/m³ respectively. The increase in internal energy of 4 kg water when it is heated from 4°C to 20°C i s____J. (Specific heat capacity of water = 4.2 × 10³ J·kg⁻¹·°C⁻¹ and 1 atmospheric pressure = 10⁵ Pa)