ICSE Class 10 Answered

Let whole of the ice melts and let the final temperature of the mixture be T^oC.

Amount of heat energy gained by 10g of ice at -10^oC to raise its temperature to 0^oC= 10x10x2.1=210J

Amount of heat energy gained by 10g of ice at 0^oC to convert into water at 0^oC=10x336=3360 J

Amount of heat energy gained by 10g of water (obtained from ice) at 0^oC to raise its temperature to T^oC = 10x4.2x(T-0)=42T

Amount of heat energy released by 10g of water at 10^oC to lower its temperature to T^oC = 10x4.2x(10-T)=420-42T

Heat energy gained = Heat energy lost

210 + 3360 + 42T = 420-42T

T = -37.5^oC

This cannot be true because water cannot exist at this temperature.

 So whole of the ice does not melt. Let m gm of ice melts. The final temperature of the mixture becomes 0^oC.

 So, amount of heat energy gained by 10g of ice at -10^oC to raise its temperature to 0^oC= 10x10x2.1=210J

Amount of heat energy gained by m gm of ice at 0^oC to convert into water at 0^oC=mx336=336m J

 Amount of heat energy released by 10g of water at 10^oC to lower its temperature to 0^oC = 10x4.2x(10-0)=420

Heat energy gained = Heat energy lost

210 + 336m = 420

m = 0.625 gm