A calorimeter is a container that is insulated from the outside, so a negligible amount of energy enters or leaves the container when it is closed.

Consider a copper calorimeter with mass 0.100 kg that contains 0.160 kg of water and 0.018 kg of ice, all in thermal equilibrium at atmospheric pressure. If 0.750 kg of lead at a temperature of 255 ∘C is dropped into the calorimeter, what is the final temperature?

Assume that no heat is lost to the surroundings.

This is a heat balance question with negligible heat losses to the surroundings.

Sum of heat losses = Sum of the heat gains

We are required to find the final temperature of the calorimeter system T1?

we were given

C = specific heat capacities of Copper c, Water w, Ice i and Lead l

m = masses as mc = 0.1kg, mw = 0.16kg, mi=0.018kg, ml=0.75kg,

T = Temperature of the components, Lead Tl = 225C and at ambient pressure, Temp. To of the water, ice and copper = 25C

Since, at thermal equilibrium after adding the Lead, the lead temperature Tl decreases while copper, water and ice temp decrease, so we have respective heat losses 'q' as,

qc + qw + qi + ql = 0

which means that

(mc x Cc x ΔTC) + (mw x Cw x ΔTC) + (mi x Ci x ΔTC) + (ml x Cl x ΔTC) = 0

(0.1x390x (T1 - 25)) + (0.16x4190x (T1 - 25)) + (0.018x4190x (T1 - 0)) + (0.750x130x (T1 - 225)) = 0

882.32T1 - 41558 = 0

T1 = 47.1K

Hence, the final temperature of the calorimeter system is 47.1K