Question

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at $100^{\circ} C$ , while the other one is at $0^{\circ} C$. If the two bodies are brought into contact, then, assuming no heat loss, the final common temperature is -

• A. $50^{\circ} C$
• B. more than $50^{\circ} C$
• C. less than $50^{\circ} C$ but greater than $0^{\circ} C$
• D. $0^{\circ} C$

Answer 1

The Correct Option is B

Heat Capacity and Temperature Relationship 

As the temperature increases, the heat capacity also increases. Hence, the heat capacity of the second substance is greater than the first. Let the heat capacities be \( c_1 \) and \( c_2 \) for the first and second substances, respectively, and let the common temperature be \( T \). The equation for heat transfer is:

\(mc_1 (T - 0) = mc_2 (100 - T)\)

We can simplify this equation to:

\(\frac{T}{100 - T} = \frac{c_2}{c_1} > 1\)

This implies:

\(c_2 > c_1\)

Since \( \frac{T}{100 - T} > 1 \), it follows that:

\(T > 50\)

Conclusion:

The temperature \( T \) must be greater than 50 for the heat capacity of the second substance to be greater than the first.