Thermal Physics Specific Heat Capacity and Specific Latent Heat Question (in description)

Question

Please could someone check my answers to questions I have been doing for revision purposes? I do not have a mark scheme. Thank you!

Ice of mass 22g at temperature -12C is taken from a freezer and placed in a polystyrene cup containing water at a temperature 22C. 

specific heat capacity of ice = 2100 Jkg-1K-1

specific latent heat of fusion of ice = 3.3x105 Jkg-1

(a) Calculate the quantity of heat needed:

(i) to raise the temperature of the ice from -12 degrees C to 0 degrees C 

Answer I calculated: 554.4J (is this correct?)

(ii) to change the ice to water without an increase in temperature. 

Answer I calculated: 7300J (is this correct?)

b) The temperature of the water in the cup falls after the ice as been added. 

Specific heat capacity of water = 4200 J kg-1 K-1. 

(i) Calculate the mass of the water in the cup if the lowest temperature reached by the water is 8 degrees C.

Answer I calculated: 140g (2s.f.) (is this correct?)

II) State an assumption made in part i

Answer I gave: All energy given out by water is transferred to ice. No heat loss to the surroundings.

Answer 1

Raise ice from -12º to 0º

q = mC∆T = (22 g)(2.1 J/gº)(12º) = 554.4 J YOU ARE CORRECT

Melt ice without change in temperature = phase change

q = m∆Hfusion = (22g)(330 J/g) = 7260 J = 7300 J (2 sig. figs.) YOU ARE CORRECT

heat gained by ice = heat lost by water

554 J + 7300 J = (m)(4.2 J/gº)(∆T)

7854 J = (m)(4.2 J/gº)(14º)

m = 134 g Not sure where you got 140 g unless I mis-interpreted the question.

I agree with your assumption that no heat was lost to the surroundings.

Answer 2

Emma C

I have answered similar questions on my YouTube channel Mr. A's Physics.

The video is labeled: Law of heat exchange harder problems solved

https://www.youtube.com/watch?v=_mrzX18jbCg&list=PLqb1ya7zRMRBTSOZA3OTCKJmog7vJ_0AO&index=11

Mr. A