Heat energy of 184 kJ is given to ice of mass 600 g at -12° C. Specific heat of ice is 2222.3 J kg^(-1°) C⁻¹ and latent heat of ice in 336 kJ/kg⁻¹
A. Final temperature of system will be 0°C.
B. Final temperature of the system will be greater than 0°C.
C. The final system will have a mixture of ice and water in the ratio of 5 : 1.
D. The final system will have a mixture of ice and water in the ratio of 1 : 5.
E. The final system will have water only.
Choose the correct answer from the options given below :

Solution

Physics sir · 4 steps

Spend the heat in stages: first warm the ice to 0°C, then see how much of it the leftover heat can melt.

1. Warm ice to 0°C. Heat needed to raise 600 g of ice from -12°C to 0°C is mcΔ T = 0.6 × 2222.3 × 12 ≈ 16 000 J = 16 kJ.
2. Heat left over. 184 - 16 = 168 kJ remains. Melting all the ice would need 0.6 × 336 = 201.6 kJ, which is more than 168 kJ. So not all the ice melts, and the temperature stays at 0°C.

   m_(melted) = Q/L = (168 kJ)/(336 kJ kg⁻¹) = 0.5 kg

3. Ice to water ratio. 500 g has melted into water and 600 - 500 = 100 g is still ice. So ice : water = 100 : 500 = 1 : 5.
4. So. The final temperature is 0°C (A) and ice and water are in the ratio 1 : 5 (D). The answer is (d).

The idea to keep. In ice problems, compare the heat supplied with each stage's need in order: warm to 0°C, then melt. If the heat runs out during melting, the mixture sits at exactly 0°C.

Answer from the NTA final answer key. Solution by PrepWiser.