Question

A mass of 40g of brass of specific heat capacity 0.85 Jg^-1 K^-1 is heated in an oven and then quickly transferred into 240g of water at 30°C in a calorimeter of mass 60g and specific heat capacity 0.4 Jg^-1 K^-1. If the final temperature is 50°C. What was the temperature of the oven?

Answer 1

Hot Body (Brass)	Cold Body (Water)	Copper Calorimeter	Note
m1 = 40 g	m2 = 240 g	m3 = 60 g	(i) Temperature of oven is same as hot body
θ1 = ? c1 = 0.85 J g-1k-1	θ2 = 30°C c2 = 4.2 J g-1 k-1	θ2 = 30°C c3 = 0.4 J g-1k-1	(ii) Temperature of calorimeter is same as cold body.

Final temperature, θ = 50°C

∴ Fall in temperature of hot body = θ₁ - θ = (θ₁ -  50)

Rise in temperature of cold body = θ - θ₂ = (50 - 30) = 20

Heat lost by hot body = Heat gained by cold body + Copper calorimeter

m₁C₁ (θ₁ - θ) = m₂C₂ (θ₁ - θ) + m₃C₃ (θ₁ - θ) 

40 × 0.85 × θ - 50 = (240 × 4.2 × 20) + (60 × 0.4 × 20)

40 × 0.85 (θ - 50) = (20160 + 480)

(θ - 50) = `20640/(40 xx 0.85)`

θ = 607.05 + 50 = 657.05°C

Temperature of oven = 657.05°C