Question

1 gm of ice at 0°C is mixed with 1 gm of water at 100°C. At thermal equilibrium, the temperature of the mixture will be:

• A. 50°C
• B. 20°C
• C. 10°C
• D. 100°C

Hint:

In problems involving the mixing of ice and water, always consider the heat lost by the warm substance and the heat gained by the cold substance. Use the latent heat formula for ice melting to find the equilibrium temperature.

Answer 1

The Correct Option is C

The problem involves the mixing of ice at 0°C with water at 100°C. To determine the final temperature of the mixture, we must consider the heat exchange between the ice and the water. When ice melts, it absorbs heat (latent heat of fusion), and the water loses heat as it cools down. Using the principle of conservation of energy, we can set up the equation: \[ Q_{\text{mix}} = Q_w - \frac{L_i}{C_w} \] Where: - \( Q_{\text{mix}} \) is the heat exchange, - \( Q_w \) is the heat lost by the water, - \( L_i \) is the latent heat of fusion of ice, - \( C_w \) is the specific heat capacity of water. By solving the equation, we find that the final temperature of the mixture is 10°C.