Question

How much ice is needed to make ice tea at a temperature of 5⁰ C from 140 grams of hot tea at 65⁰ C contained in a glass container of 50 gm with specific heat equal to 0.2 cal/gm⁰ C. Treat the tea as colored water.

Answer 1

Answer: 692.307 gm of ice is needed

Explanation:

Given data:

• Hot Tea : Mass MHT = 140 gm

CHT = 1 cal/gm 0C

Inital Temperature = 650 0C

Final temperature = 50 0C

• Glass container : Mass MG = 50 gm

CHT = 0.2 cal/gm 0C

Inital Temperature = 650 0C (we assumed)

Final temperature = 50 0C

We assume that initial temperature of ice is 0 0C and Let "mice" be the mass of ice needed

Heat Losssed = Heat Gained

i.e Qlossed  = Qgained

Here the energy is lossed by hot tea and glass container . And the energy is gained by the ice.

So

where L is the latent heat of fusion = 80 cal/gm for ice and MICE-WATER is the mass of the water formed when ice melts ( which is same as mass of ice , MICE)