Question

A hot object is dropped into a thermally insulated container of water, and the object and water are then allowed to come to thermal equilibrium. The experiment is repeated twice, with different hot objects. All three objects have the same mass and initial temperature and the mass and initial temperature of the water are the same in the three experiments. For each of the experiments, Fig. 18-29 gives graphs of the temperatures Tof the object and the water versus time t. Rankthe graphs according to the specific heats of the objects, greatest first.

Short answer

The rank of the given graphs according to the specific heats of the objects is $\mathrm{Graph}\left(\mathrm{c}\right)>\mathrm{Graph}\left(\mathrm{b}\right)>\mathrm{Graph}\left(\mathrm{a}\right)$.

Step-by-step solution

The given data

1. The container is thermally isolated.
2. All the three objects have same mass m.
3. All the three objects have same initial temperature T.
4. The mass of water is same in all the three experiments.
5. The initial temperature of water is same in all the three experiments.
6. The Figure 18-29.

Understanding the concept of heat

The process of thermal energy exchange caused by temperature differences is known as heat transfer. By using the information from the given Figures 18-29 in the formula for heat, we can find the ranks of the given graphs according to the specific heat of the objects.

Formula:

The energy transferred as heat to the surroundings,$\mathrm{Q}=\mathrm{cm}∆\mathrm{T}$ …(i)

Where,

m is mass, c is specific heat ,$∆\mathrm{T}$ is change in temperature

Calculation of the rank of the objects according to the specific heat

FromFigure 18-29, we can see that there are two curves in each graph. The upper curve shows the temperature T with respect to time t of the corresponding hot object, and the lower curveshows the temperature T with respect to time t of the water in the container. These two curves meet at a temperature T, at which equilibrium occurs, and it is represented by a horizontal line at that temperature T.

It is given that the temperature difference is $∆\mathrm{T}={\mathrm{T}}_{\mathrm{f}}-{\mathrm{T}}_{\mathrm{i}}$, where, T_f is the final temperature of the corresponding object, and T_i is the initial temperature which is same for all the given objects.

Thus, the value of change in temperature $∆\mathrm{T}$depends on the value of the final temperature T_f.

From Figure 18-29, in Graph (a) we can see that the final temperature T_f of the object is less than that in Graph (b) and also the final temperature T_f of the object in Graph (b) is less than that in Graph (c).

The hot object loses temperature in water to get the equilibrium state. Thus, the change in temperature$∆\mathrm{T}$ of the object in Graph (a) is greater than that in Graph (b) and also, the change in temperature$∆\mathrm{T}$of the object in Graph (b) is greater than that in Graph (c).

From figure 18-29, we see that the loss of heat Q of the corresponding objects is the same for time t in all three cases.

Thus, in Figure 18-29, the specific heat c for the object in Graph (a) is less than that in Graph (b) and also. The specific heat c for the object in Graph (b) is less than that in Graph (c) considering equation (i).

Therefore, the rank of the given graphs according to the specific heat of the objects is $\mathrm{Graph}\left(\mathrm{c}\right)>\mathrm{Graph}\left(\mathrm{b}\right)>\mathrm{Graph}\left(\mathrm{a}\right)$.