Problem 156 - Master Resource Book in JEE Main Physics

Question

Assertion Two bodies at different temperature, if brought in thermal contact do not necessary settle to the mean temperature. Reason The two bodies may have different thermal capacities.

Step-by-Step Solution

Answer

The assertion and reason are correct and the reason explains the assertion.

Step 1: Understand the Assertion

The assertion states that if two bodies at different temperatures are brought into thermal contact, they might not necessarily reach a mean (average) temperature. It implies that there are factors influencing the final temperatures other than simply being brought into contact.

Step 2: Analyze the Reason

The reason given is that the two bodies might have different thermal capacities. Thermal capacity affects how an object can absorb or release heat, meaning two objects with different thermal capacities will absorb or release different amounts of heat even if they have the same change in temperature.

Step 3: Link Assertion and Reason

The reason effectively supports the assertion. Different thermal capacities mean that even if the objects exchange heat, the amount of heat exchange is influenced by their capacities. Hence, they do not necessarily reach the average of their initial temperatures.

Step 4: Check Conceptual Understanding

The final temperature of the two bodies when brought into contact depends on their initial temperatures and thermal capacities. The formula to determine the equilibrium temperature can be expressed as \((m_1 \cdot c_1 \cdot T_1 + m_2 \cdot c_2 \cdot T_2) / (m_1 \cdot c_1 + m_2 \cdot c_2)\), where \(m\) is mass, \(c\) is specific heat capacity, and \(T\) is initial temperature. This formula shows that the equilibrium temperature isn't merely the average of \(T_1\) and \(T_2\) unless \(m_1 \cdot c_1 = m_2 \cdot c_2\).

Step 5: Conclusion

Therefore, the assertion is correct, and the reason provides a valid explanation. Different thermal capacities prevent the bodies from simply reaching their mean temperature when brought into thermal contact.

Key Concepts

Thermal Capacity

Thermal capacity is a fundamental concept that explains how much heat an object can store. It is the amount of heat needed to change an object's temperature by 1°C (or 1 K).
You can think of thermal capacity as an object's ability to absorb heat before its temperature changes significantly.
Key points to know about thermal capacity:

• It depends on the object's size—larger objects usually have higher thermal capacity.
• An object with a high thermal capacity can absorb a lot of heat without a large temperature change.
• Thermal capacity is measured in joules per degree Celsius (J/°C).

Therefore, when two bodies with different thermal capacities are in thermal contact, they won't necessarily reach the mean temperature of both bodies. Instead, the body with the higher thermal capacity will have a more gradual temperature change as it is able to absorb more heat.

Heat Exchange

Heat exchange occurs when two objects at different temperatures come into contact. Usually, heat flows from the warmer object to the cooler one until thermal equilibrium is reached.
However, the heat exchange process depends significantly on the thermal capacities of the interacting bodies.
Important aspects of heat exchange include:

• Heat always flows from hot to cold.
• Even if the two objects are brought into contact, if their thermal capacities differ, they won’t simply reach an average temperature.
• The heat exchanged is proportional to the product of mass, specific heat, and change in temperature.

The equation describing the final temperature once thermal equilibrium is achieved involves balancing the heat gained by one object with the heat lost by the other.

Specific Heat Capacity

Specific heat capacity is a more detailed way to look at how a material absorbs heat. It describes how much heat per unit mass is needed to raise the temperature of a substance by 1°C.
Specific heat capacity is unique for each kind of material.
Why is specific heat capacity important?

• It helps explain why heating different materials requires different amounts of energy.
• Materials with high specific heat capacity can absorb more heat without a big temperature jump.
• It's expressed in units of joules per gram per degree Celsius (J/g°C).

In equations for heat exchange, specific heat capacity is crucial. If two bodies have different masses and specific heat capacities, these factors determine how much heat each will absorb or release, which in turn influences the final equilibrium temperature.