A sphere A is placed at smooth table. An another sphere B is...

A sphere $A$ is placed at smooth table. An another sphere $B$ is suspended as shown in figure. Both spheres are identical in all respects. Equal quantity of heat is supplied to both spheres. All kinds of heat loss are neglected. The final temperatures of $A$ and $B$ are $T_{A}$ and $T_{B}$ respectively, then : (a) $T_{A}=T_{B}$ (b) $T_{A}>T_{B}$ (c) $T_{A}<T_{B}$ (d) none of these

A sphere $A$ is placed at smooth table. An another sphere $B$ is suspended as shown in figure. Both spheres are identical in all respects. Equal quantity of heat is supplied to both spheres. All kinds of heat loss are neglected. The final temperatures of $A$ and $B$ are $T_{A}$ and $T_{B}$ respectively, then : (a) $T_{A}=T_{B}$
(b) $T_{A}>T_{B}$
(c) $T_{A}<T_{B}$
(d) none of these

Key Concepts

Effective Heat Capacity

The effective heat capacity of a system refers to the amount of heat required to achieve a unit change in temperature, taking into account not only the inherent properties of the material but also any additional energy expenditures such as work done against external forces. When a part of the supplied heat is diverted to perform work (for example, raising the center of mass), the effective heat capacity increases, and the temperature rise for a given quantity of heat becomes lower.

Work in Thermodynamic Processes

In thermodynamic processes, work is done when a system changes its configuration, such as expanding against a force like gravity. When heat is supplied to a system, part of the energy may be used to perform work rather than increasing the system’s internal energy. Understanding how and where this work is done is essential in analyzing energy distribution and the resulting temperature changes.

Thermal Expansion

Thermal expansion is the phenomenon where a material increases in size when its temperature rises. This occurs because its constituent particles vibrate more vigorously, causing the average separation between them to increase. In thermodynamics, thermal expansion plays a key role in systems where the expansion leads to work being done, which in turn affects how the energy added to the system is partitioned.

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. When an object expands or moves in such a field, there can be changes in the energy associated with its height. This concept is crucial when analyzing systems where thermal expansion causes a shift in the center of mass, thereby requiring or releasing energy in the form of gravitational work.

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