Question

A container with a temperature T1 of 15°C is submerged in a bucket of hot water with a temperature T2 of 37°C. An identical container with a temperature of T1 is submerged in an identical bucket of water with a temperature of T2. If the amounts of energy transferred as heat between the containers and the water are the same in both cases, which of the following statements is true?

Answer 1

Answer:

d. T1 = 7°C; T2 = 29°C

Explanation:

The temperature of a substance is a measure of the average kinetic energy of is particle: in fact, the two quantities are proportional to each other.

Moreover, heat is always transferred spontaneously from a hotter object (higher temperature) to a colder object (lower temperature).

In this problem, we have a container placed in contact with a bucket of hot water: heat flows from the hot water to the container, until the two are at the same  temperature.

The amount of energy transferred between the two is proportional to the initial temperature difference between the container and the water:

$Q\propto \Delta T$

Since in the two situations the amount of energy transferred is the same, then it means that the temperature difference between the two substances is the same in the two situations. So we can write:

$T_2-T_1=37^{\circ}-15^{\circ}=22^{\circ}$

And from the choices given, we see that the only option that satisfies this condition is

$T_1=7^{\circ}C, T_2=29^{\circ}C$