F3 physics question in book

Question

A student adds 0.2 kg of ice at 0C into 0.4kg of hot tea at 80C.

What is the final temperature of the mixture ?

(The specific heat capacity of tea is 4000 J kg-1 C-1 )


thank you

Answer 1

Final temperature = ToC.

Heat gained for 0oC ice to 0oC water then ToC water
= mL + mcΔT
= (0.2)(334000) + (0.2)(4200)(T - 0)
= 66800 + 840T

Heat lost for 80oC of tea to ToC of tea
= mcΔT
= (0.4)(4000)(80 - T)
= 128000 - 1600T

Since net heat change = 0,
66800 + 840T = 128000 - 1600T
2440T = 61200
Final temperature T = 25.1oC