In an experiment to verify Newton’s law of cooling, a graph is plotted between, the temperature difference (ΔT) of the water and surroundings and time as shown in figure. The initial temperature of water is taken as 80ºC. The value of \(t_2\) as mentioned in the graph will be ______.
According to Newton's law of cooling, the rate of cooling is proportional to the temperature difference between the object and its surroundings. This is mathematically expressed as: \(\frac{d(ΔT)}{dt} = -k ΔT\) where \(k\) is the cooling constant.
The graph shows an exponential decay of the temperature difference, confirming this relationship. From the graph, observe the time \(t_2\) where the temperature difference \(ΔT\) becomes 20°C.
ΔT (°C)
Time (minutes)
60
0
20
t_2
The graph shows that at \(t = 0\), \(ΔT = 60°C\). At \(t = t_2\), \(ΔT = 20°C\).
According to the graph, \(t_2\) is clearly marked as 16 minutes, aligning with the expected range of 16 to 16. Thus, \(t_2 = 16\) minutes is confirmed correct.
