Question

If a liquid takes 30 s in cooling from ${95}^{0}C$ to ${90}^{0}C$ and 70 s in cooling from ${55}^{0}C$ to ${50}^{0}C$ then temperature of room is:

• A. ${16.5}^{0}C$
• B. ${22.5}^{0}C$
• C. ${28.5}^{0}C$
• D. ${32.5}^{0}C$

Answer 1

The correct option is B ${22.5}^{0}C$

T₀ = room temperature, T = temperature of the liquid at time t

$\frac{dQ}{dt}$= $\frac{dT}{dt}$ = rate of cooling = $-k[T-T₀]$ --- (1)

$\frac{dT}{[T-T₀]}=-kdt$

=> $Ln\frac{T₂-T₀}{T₁-T₀}=-kt$

$(T₂-T₀)=(T₁-T₀)\times e^{-kt}$