Question

4kg of ice at -15°c is added to 5 kg of water at 15°C. The temperature of the resulting mixture is

a) -15°C b) 0°C c) 5°C d) 15°C​

Answer 1

•Given:- 4kg of ice at -15°c is added to 5 kg of water at 15°C.

• To find:-The temperature of the resulting mixture

• Solution:-

Heat given by water to cool upto 0°C = mCΔT = 5000× 1 × (15 – 0) = 75000 cal.

Heat taken by ice to melt = 4000 × 80 = 32000cal

(as latent heat of fusion of ice = 80 cal/gm)

so, temperature of mixture cannot be 0°C

Let, temperature of mixture = θ°C.

so,5000 × 1(15 – θ) = 320000 + 4000 × 1 × (θ – 0)

5000 (15 – θ) = 800 + 4000(θ)

or, 75000 – 5000θ = 320000 - 4000θ

or,43 = 9θ

So, θ = 43/9°C =4.7°C ≈ 5°C

So the final answer is c)5°C