A metal container of hot liquid is left to cool in a laboratory. The temperature of the liquid, \(T\

Question

A metal container of hot liquid is left to cool in a laboratory. The temperature of the liquid, $T$ °C, after $n$ minutes is given by $T = a\mathrm{e}^{-kn} + 15$, where $a$ and $k$ are constants. The table below shows the measured values of $T$ and $n$.

$n$ (minutes)	$10$	$20$	$30$	$40$	$50$
$T$ °C	$66.9$	$46.5$	$35.1$	$27.2$	$22.4$

Plot $\ln(T - 15)$ against $n$ and draw a straight line graph to illustrate the information.[1]
Use your graph to estimate
1. the value of $k$[2]
2. the number of minutes it takes for the temperature of the liquid to drop to $40 \%$ of its initial value.[3]

Accepted Answer

(a) Straight-line plot of $\ln(T-15)$ against $n$. (b)(i) $k\approx0.049\ \text{min}^{-1}$. (ii) About $25$ minutes (graph estimate).

2024 GESS PRELIMS P1 Q14

2024 GESS PRELIMS P1 Q14

Solution:

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