Thermodynamics - Cooling of a liquid. The temperature of a liquid is measured every 20 minutes and the results recorded in the table below. \begin{tabular}{lrllllrr} \hline Time \((\min )\) & 0 & 20 & 40 & 60 & 80 & 100 & 120 \\ Temp \(\left({ }^{\circ} \mathrm{C}\right)\) & 96 & 88 & 81 & 76 & 72 & 70 & 68 \\\ \hline \end{tabular} Calculate the rate of decrease of temperature. in units of \({ }^{\circ} \mathrm{C}\) per minute: (a) in the first 20 minutes (b) in the first 40 minutes (c) in the first 60 minutes (d) in the last 60 minutes (e) in the last 20 minutes In each case express your answer as a fraction in its simplest form.

The table provides temperature readings for a liquid taken every 20 minutes. We have the following data: Time ( minutes ) : 0, 20, 40, 60, 80, 100, 120 Temp ( °C ) : 96, 88, 81, 76, 72, 70, 68

To calculate the rate of decrease of temperature in the specified intervals, we need to calculate the change in temperature and divide it by the duration of the interval (in minutes). Here are the calculations for each time interval: (a) First 20 minutes: Rate = (Temperature at 20 min - Temperature at 0 min)/(20 min - 0 min) Rate = (88 - 96)/20 (b) First 40 minutes: Rate = (Temperature at 40 min - Temperature at 0 min)/(40 min - 0 min) Rate = (81 - 96)/40 (c) First 60 minutes: Rate = (Temperature at 60 min - Temperature at 0 min)/(60 min - 0 min) Rate = (76 - 96)/60 (d) Last 60 minutes: Rate = (Temperature at 120 min - Temperature at 60 min)/(120 min - 60 min) Rate = (68 - 76)/60 (e) Last 20 minutes: Rate = (Temperature at 120 min - Temperature at 100 min)/(120 min - 100 min) Rate = (68 - 70)/20

Now, let's express the rates of decrease as fractions in their simplest forms: (a) First 20 minutes: Rate = (88 - 96)/20 = (-8)/20 Simplified Rate: -2/5 °C per minute (b) First 40 minutes: Rate = (81 - 96)/40 = (-15)/40 Simplified Rate: -3/8 °C per minute (c) First 60 minutes: Rate = (76 - 96)/60 = (-20)/60 Simplified Rate: -1/3 °C per minute (d) Last 60 minutes: Rate = (68 - 76)/60 = (-8)/60 Simplified Rate: -2/15 °C per minute (e) Last 20 minutes: Rate = (68 - 70)/20 = (-2)/20 Simplified Rate: -1/10 °C per minute So, the rates of decrease of temperature for the specified intervals are: -2/5, -3/8, -1/3, -2/15, and -1/10 °C per minute.