If water at 100^ C cools in 10 minutes to 80^ C and to 65^ C in the next 10 minutes, then the room temperature will be ...

Step-by-step solution

Using Newton's law of cooling: T₁ - T₂ t = K ( T₁ + T₂ 2 - T₀ ) For the first 10 minutes: 100 - 80 10 = K ( 100 + 80 2 - T₀ ) 2 = K(90 - T₀) For the next 10 minutes: 80 - 65 10 = K ( 80 + 65 2 - T₀ ) 1.5 = K(72.5 - T₀) Dividing the two equations: 2 1.5 = 90 - T₀ 72.5 - T₀ 4 3 = 90 - T₀ 72.5 - T₀ 4(72.5 - T₀) = 3(90 - T₀) 290 - 4T₀ = 270 - 3T₀ T₀ = 20^ C Answer: 20^ C