To Study The Relationship Between Temperature Of Hot Body And Time By Plotting A Cooling Curve - Practice Questions & MCQ

Aim:
To study the relationship between the temperature of a hot body and time by plotting a cooling curve.

Apparatus:
Newton's law of cooling apparatus (a thin-walled copper calorimeter suspended in a double walled
enclosure), two thermometers, clamp and stand, stop clock/watch.

Theory:
Newton's law of cooling, states that the rate of cooling (or rate of loss of heat) of a body is directly
proportional to the temperature difference between the body and its surroundings, provided the
temperature difference is small.

$
\frac{d Q}{d t} \propto\left(T-T_0\right)
$

For a body of mass m , specific heat s , temperature T kept in surrounding of temperature $T_0$. Then
Rate of cooling, $\frac{d Q}{d t}=m s \frac{d T}{d t}$
Hence, $\frac{d T}{d t} \propto\left(T-T_0\right)$
As time increase, $T$ decreases, hence rate of fall of temperature $\left(\frac{d T}{d t}\right)$ must also decrease.

$
\begin{aligned}
& \frac{d Q}{d t} \alpha\left(\theta-\theta_o\right) \\
& \frac{d Q}{d t}=m s \frac{d \theta}{d t}
\end{aligned}
$
 

Procedure:
1. Fill the space between double wall of the enclosure with water and put the enclosure on a laboratory
table.

2. Fill the calorimeter two-third with water heated to about $80^{\circ} \mathrm{C}$.
3. Suspend the calorimeter inside the enclosure along with a stirrer in it. Cover it with a wooden lid having a hole in its middle.
4. Suspend from clamp and stand, one thermometer in enclosure water and the other in calorimeter water.
5. Note least count of the thermometers.
6. Set the stop clock/watch at zero and note its least count.
7. Note temperature $T_0$ of water in enclosure.
8. Start stiring the water in calorimeter to make it cool uniformly.
9. Just when calorimeter water has some convenient temperature reading (say $70^{\circ} \mathrm{C}$ ), note it and start the stop clock/watch.
10. Continue stirring and note temperature after every one minute. The temperature falls quickly in the beginning.
11. Note enclosure water temperature after every five minutes.
12. When fall of temperature becomes slow note temperature at interval of two minutes for 10 minutes and then at interval of 5 minutes.
13. Stop when fall of temperature becomes very slow.
14. Record your observations as given ahead.

Calculations:
1. Temperature of water in enclosure will be found to remain same. If not then take its mean as To.
2. Find temperature difference $\left(T-T_0\right)$.
3. Plot a graph between time $t$ and temperature $T$, taking $X$-axis and $T$ along $Y$ - axis. The graph is called the Cooling cooling curve of the liquid.

Result:
The temperature falls quickly in the beginning and then slowly as the difference of temperature goes on
decreasing.
This is an agreement with Newton's law of cooling.

Precautions:
1. Double-walled enclosure should be used to maintain surroundings at a constant temperature.
2. Stiring should remain contentious for uniform cooling.