Question

A chunk of aluminum weighing 19.1 grams and originally at 98.95°C is dropped into an insulated cup containing 80.7 grams of water at 20.69°C. Assuming that all of the heat is transferred to the water, the final temperature of the water is °C.

Answer 1

The hot body is aluminum , the cold body is water  

We know that the

Heat given out by solid

=

Heat absorbed by water

Heat capacity= m Cp (Ti- Tf)

where m is mass

Cp is specific heat

Ti is initial temp

Tf is final temp

mass of aluminum = 19.1 g

Temperature of Al solid = 98.95 DegC

mass of water = 19.1 g

Temperature of water =20.69 DegC

Cp values are not given .

So we consider

Cp of water = 4.186 J/ g degC

Cp of Al = 0.9 J/g degC

m Cp (Ti- Tf)_aluminum = m Cp (Ti- Tf)_water

19.1*0.9*(98.95-Tf) = 80.7*4.186*(Tf-20.69)

Solving for Tf

17.19*(98.95-Tf) = 337.81*(Tf-20.69)

98.95- Tf = 19.65 *(Tf-20.69)

Tf= 24.48 DegC

The final temperature of water is 24.59 DegC