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 of water when it is heated from 4°C to 20°C is ____ J. (specific heat capacity of water = 4.2 J/kg·K and 1 atmospheric pressure = 10⁵ Pa)

Density of water at 4°C and 20°C are 1000 kg/m³ and 998 kg/m³ respectively

Q. 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 of water when it is heated from 4°C to 20°C is ____ J.

(specific heat capacity of water = 4.2 J/kg·K and 1 atmospheric pressure = 10⁵ Pa)

(A) 268799.2

(B) 315826.2

(D) 258700.8

Correct Answer: 268799.2

Explanation

Increase in internal energy is given by

\[ \Delta U = Q - W \]

Heat supplied:

\[ Q = mc\Delta T \]

\[ Q = 4 \times 4200 \times (20 - 4) \]

\[ Q = 268800 \text{ J} \]

Now calculate work done due to volume change.

Initial volume at 4°C:

\[ V_1 = \frac{m}{\rho_1} = \frac{4}{1000} = 0.004 \text{ m}^3 \]

Final volume at 20°C:

\[ V_2 = \frac{4}{998} \approx 0.004008 \text{ m}^3 \]

Change in volume:

\[ \Delta V = V_2 - V_1 = 0.000008 \text{ m}^3 \]

Work done at atmospheric pressure:

\[ W = P\Delta V = 10^5 \times 0.000008 = 0.8 \text{ J} \]

Hence,

\[ \Delta U = 268800 - 0.8 = 268799.2 \text{ J} \]

Therefore, the increase in internal energy is 268799.2 J.

Explanation

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