Certain quantity of water cools from 70°C to 60°C in the

Certain quantity of water cools from 70°C to 60°C in the first 5 minutes and to 54°C in the next 5 minutes. The temperature of the surroundings is:

Let the temperature of surroundings be θ₀
By Newton's law of cooling

θ₁ - θ₂	= k		θ₁ + θ₂	- θ₀
t			2

⇒	70 - 60	= k		70 + 60	- θ₀
	5			2

⇒ 2 = k [65 – θ₀] ...(i)

Similarly,	60 - 54	= k		60 + 54	- θ₀
	5			2

⇒	6	= k[57 - θ₀] .............(ii)
	5

By dividing (i) by (ii) we have

	10	=	65 - θ₀	⇒ θ₀ = 45°
	6		57 - θ₀