1. A well-insulated 7.00 kg glass bowl [c=840J/(kg. o C)] contains 16.0 kg of pu

Question

1. A well-insulated 7.00 kg glass bowl

[c=840J/(kg.oC)] contains 16.0 kg of punch,

(essentially water)

[c=4186 J/(kg.oC)] , at 25 oC. Now 2.50 kg of ice

[c= 2100 J/(kg.oC)] is dumped into the punch.

The ice has an initial temperature of -20oC and

the latent heat of fusion for H2O (at 0oC)

is 333,000 J/kg. Answer the following questions

in either order (a then b, or b then a) using

the basic laws of calorimetry.

a) Show that all the ice will melt when thermal

equilibrium is reached. [Hint: calculate the heat

needed to heat the ice to the melting point and then

to melt it all; and compare it with your calculation

for how much heat could be released by the punch

(plus the bowl) coming down

to 0 oC]. Make sure your logical sequence is

complete. (10)

B) Assuming that all the ice will melt in the end,

calculate the final temperature of the punch after

the thermal equilibrium is reached.

Show all your steps and calculations. (10)

Explanation / Answer

Q1 .

part a:

the ice will melt completely if the punch at 25 degree celcius and the glass at 25 degree

release enough heat to bring the temperature of ice from -20 degree celcius to 0 degree celcius

and convert it completely to water at 0 degree celcius.

heat required to increase the temperature of ice from -20 degree celcius to 0 degree celcius

=mass*specific heat of ice*temperature difference

=2.5*2100*(0-(-20))=105000 J

heat required to melt the ice at 0 degree celcius completely=mass*latent heat of fusion of ice

=2.5*333000=832500 J

then total energy required to melt ice completely=832500+105000=937500 J

heat released by punch and glass bowl when the temperature decreases from 25 degree celcius to 0 degree celcius

=mass of bowl*specific heat of glass*temperature difference+mass of punch*specific heat of water*temperature difference

=7*840*(25-0)+16*4186*(25-0)=1821400 J

as 1821400 > 937500

==>all the ice will be completely melted.

part b:

let final temperature at equilibrium is T degree celcius.

then at that point,

heat released by punch + heat released by glass bowl=heat required to melt the ice completely + heat required to increase temperature of melted water from 0 degree celcius to T

==>16*4186*(25-T)+7*840*(25-T)=937500+2.5*4186*(T-0)

==>16*4186*25+7*840*25-937500=T*(16*4186+7*840+2.5*4186)

==>T=883900/83321=10.6083 degree celcius

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