Question 281: Thermodynamics & KTG

Question

A body cools in 7 minutes from $$60^{\circ} \mathrm{C}$$ to $$40^{\circ} \mathrm{C}$$. The temperature of the surrounding is $$10^{\circ} \mathrm{C}$$. The temperature of the body after the next 7 minutes will be:

Accepted Answer

Newton's law of cooling states that the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings. The average rate of cooling can be represented as:
$$\frac{T_1-T_2}{t} = K \left(\frac{T_1+T_2}{2} - T_sight)$$
where:
$T_1$ and $T_2$ are the initial and final temperatures of the body,
$t$ is the time it takes for the body to cool from $T_1$ to $T_2$,
$T_s$ is the temperature of the surroundings, and
$K$ is a constant of proportionality.
In the first 7 minutes, the body cools from $60^\circ C$ to $40^\circ C$, and the surrounding temperature is $10^\circ C$. So, the first equation is:
$$\frac{60-40}{7} = K \left(\frac{60+40}{2} - 10ight) 	ag{1}$$
In the next 7 minutes, the body cools from $40^\circ C$ to $T^\circ C$, with the same surrounding temperature. So, the second equation is:
$$\frac{40-T}{7} = K \left(\frac{40+T}{2} - 10ight) 	ag{2}$$
Solving equation (1) for $K$ and substituting into equation (2) will give the temperature $T$ after the next 7 minutes:
$$T = 28^\circ C$$

Answer

$$34^{\circ} \mathrm{C}$$

Answer

$$28^{\circ} \mathrm{C}$$

Answer

$$32^{\circ} \mathrm{C}$$

Answer

$$30^{\circ} \mathrm{C}$$

Thermodynamics & KTG

A body cools in 7 minutes from $60^{\circ} \mathrm{C} to 40^{\circ} \mathrm{C}. The temperature of the surrounding is 10^{\circ} \mathrm{C}$. The temperature of the body after the next 7 minutes will be:

Choose the correct answer: