What is the final temperature, (in degree Celsius)

Question

after a 29.0 gram piece of ice at 0 degree Celsius is placed into a styrofoam cup with 119.0 grams of water initially at 74.5 degree Celsius? Assume no loss or gain of heat from the surroundings. heat of fusion of water is 333 J/g. The specific heat of H2O(l) is approximately constant at 4.184 J/gK.  

 

What is the final temperature? (in degree Celsius)

Answer 1

STUDENT, THIS PAGE IS NOT SAVING MY COMMENTS. SEND ME AN EMAIL AND I WILL SHOW YOU THE FINAL CALCULATION.

 

I will set this up for you, but YOU do the calculations.

 

m = initial mass of ice = 29.0 g

 

M = initial mass of liquid water in the cup = 119.0 g

 

T_i = initial temperature of the liquid water = 74.5°C

 

l_f = 333 J/g

 

c = 4.184 J/(gK)

 

T_e = final equilibrium temperature = ?

 

(Note: A change in temperature is the same in °C and K.)

 

This process requires 2 heat transfers.

 

(1) Melting of ice at a constant temperature of 0°C

 

Q₁ = ml_f

 

(2) Heating of melted ice from 0°C to T_e.

 

Q₂ = mc(T_e - 0°)

 

Total heat transfer into the ice is

 

Q = Q₁ + Q₂

 

Q must equal the heat flowing out of the liquid water in the cup.

 

Q = Mc(T_i - T_e) = Mc[(74.5 - T_e)°C]

 

ml_f + mc(T_e - 0°) = Mc[(74.5 - T_e)°C]

 

You know m, l_f, c, and M.  The only unknown in the equation above is T_e.  Solve for T_e.  Be careful with units.  You should be able to finish from here.