Thermodynamics Question 5
Question 5 - 25 January - Shift 1
A bowl filled with very hot soup cools from $98^{\circ} C$ to $86^{\circ} C$ in 2 minutes when the room temperature is $22^{\circ} C$. How long it will take to cool from $75^{\circ} C$ to $69^{\circ} C$ ?
(1) 2 minutes
(2) 1.4 minutes
(3) 0.5 minute
(4) 1 minute
Show Answer
Answer: (2)
Solution:
Formula: Thermal Conduction
$ \begin{aligned} & \frac{\Delta Q}{\Delta t}=-K(T-T_0) \\ & \frac{\Delta Q}{\Delta t}=-K(T _{\text{avg }}-T_0) \\ & \text{ (i) } \frac{ms \times 12}{2}=-K(\frac{98+86}{2}-22) \\ & 6=-\frac{K}{ms}[\frac{98+86}{2}-22] \\ & \quad 6=-\frac{K}{ms}[70] \quad \ldots \ldots \ldots . . \text{ (i) } \\ & \text{ (ii) } \frac{ms \times 6}{\Delta t}=-K(\frac{75+69}{2}-22) \\ & \frac{6}{\Delta t}=-\frac{K}{ms}(50) \ldots \ldots . . . . \text{ (ii) } \\ & \text{ (ii) } \div(i) \\ & \frac{6}{\Delta t(6)}=\frac{50}{70} \\ & \Delta t=\frac{7}{5}=1.4 \text{ min } \end{aligned} $
