Question

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 $69^{\circ} C$ ?

• A. 2 minutes
• B. 1 minute
• C. $1.4$ minutes
• D. $0.5$ minute

Answer 1

Answer: (C)

$1.4$ minutes

Answer 2

$\frac{Δ_Q}{Δ_t}​=−K(T−T_0​)$

$\frac{Δ_Q}{Δ_t}​=−K(T_{avg}​−T_0​)$

(i) $\frac{ms×12}{2}​=−K\;\bigg(\frac{98+86}{2}​−22\bigg)$

$6=-\frac{K}{ms}\bigg[\frac{98+86}{2}​−22\bigg]$

$6=−\frac{K}{ms}[70]$….….. (i)

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(ii) $\frac{ms×6}{\triangle_t}​=−K\bigg(\frac{75+69​}{2}−22\bigg)$

$\frac{6}{Δ_t}​=−\frac{K}{ms}​(50)$.....(ii)

(ii) ÷ (i)

$\frac{6}{Δ_t(6)}​=\frac{70}{50}​$

$Δ_t=\frac{7}{5}​$

=$1.4\;min$