Question

I need help with Number 5, Thank you!

5. Suppose 150g of ice at a temperature of 0 C are combined with 250 g of water at 70°C.in tainer. The onty heat nges are between the ice and the water. You have been asked to predict the final state of the system. Consult the appropriate tables in b the text for any numbers you need a) One possible outcome is that the system might cool down to O'C, resulting in an ice water mixture at 0°C. How much ice would have to melt if the water cools to 0°C? Does this result seem reasonable? 50 (2.6 Based on your answer to part a, describe what you think the final equilibrium state of this system will be? List all of the temperature changes and phase changes that would need to occur for this to happen. b) c) Use calorimetry techniques to determine the equilibrium state of this system. Be sure to include a heat term for each temperature change and phase change. How much water will there be (in grams)? How much ice? At what final temperature?

Answer 1

a) For the system to cool down to 0 C, a certain amount of heat energy must be provided so that only a part of ice is melted and not the whole, otherwise the equilibrium will shift from 0 C

Let us calculate the energy required to melt whole of the ice

Q = m L where L is latent heat of fusion

= 150 gms × 80cal/gms =12000 cal

The energy supplied by water at max can be

Q = m c ∆T = 250×1×70 = 17,500 cal

So yes the water has sufficient energy, first to melt the ice and then raise the temperature of the system as a whole so final equilibrium temperature will not be 0°C

b) The final state of equilibrium will be purely water and no ice and the water in a beaker will be at a temperature greater than 0°C.

c) To calculate the final equilibrium temperature,

As we have seen, after converting whole of ice into water, 17500-12000 cal = 5500 cal will still be left.

So using heat equation.

Q = m s ∆T

5500 = 400 × 1 × ∆T ( m = 250 + 150= 400 as all ice has been converted into water)

∆T = 13.75 °C

Hence the equilibrium temperature of the system will be 13.75 °C with 400gm water and 0g ice.