Object A has greater mass than object B, which is made of the same material, and the two have different temperatures. The objects are brought into thermal contact and are isolated from the outside world. Which of the following statements correctly describes their approach to thermal equilibrium? A) The temperature of object A will change more than the temperature of object B. B) The temperature of object B will change more than the temperature of object A. C) Their temperature changes will be the same. D) There is not enough information to answer this question.
The Correct Answer and Explanation is:
Correct Answer: B) The temperature of object B will change more than the temperature of object A.
Explanation:
When two objects of different temperatures are placed in thermal contact and are isolated from the environment, they exchange heat until they reach the same temperature. This state is known as thermal equilibrium.
In this case, both objects are made of the same material, which means they have the same specific heat capacity. The only difference is in their mass: object A has a greater mass than object B.
The amount of heat an object can gain or lose is given by the formula:
Q = mcΔT
where:
- Q is the heat absorbed or released,
- m is the mass,
- c is the specific heat capacity, and
- ΔT is the change in temperature.
Since the two objects are isolated from the outside world, heat lost by one is equal in magnitude to the heat gained by the other:
Q_lost by one = Q_gained by the other
Let us assume object A is hotter than object B. Because object A has more mass, it has a larger heat capacity (mc). To reach equilibrium, it needs to lose heat, but since its heat capacity is higher, its temperature does not need to drop much to transfer a certain amount of heat.
Object B, with less mass, has a smaller heat capacity, so it must increase its temperature more significantly in order to absorb the same amount of heat.
Therefore, the object with the smaller mass (object B) undergoes a larger temperature change during the approach to equilibrium. The direction of heat flow is from hot to cold, but the magnitude of temperature change depends on mass and heat capacity. Since mass is different and material is the same, the temperature of object B will change more.
Thus, the correct answer is B.
