Spherical ball A is hung down from a massless, inextensible...

Spherical ball A is hung down from a massless, inextensible string that is connected to a wall. Spherical ball B lies motionless on a horizontal floor. The same quantity of heat $Q$ is supplied to both balls. Assuming no heat losses, are the final temperatures of the balls the same? If not, estimate the difference in the final temperatures in terms of parameters of your choice. (International Physics Olympiad)

Key Concepts

Energy Partitioning in Thermal Processes

In many physical situations, the supplied energy is divided between increasing the temperature and doing work, such as lifting an object against gravity. This concept explains why systems with additional energy demands (e.g., performing work against external forces) may experience a lower temperature increase than systems where all the energy goes into raising the internal energy.

Conservation of Energy

This principle states that the total energy of an isolated system remains constant. In thermodynamics, the heat supplied to a system (assuming no losses) can be converted into changes in internal energy or do work against other forces. Understanding this concept is crucial when analyzing how different processes or setups might partition the same energy input into different forms.

Heat Capacity

Heat capacity is a material property that quantifies the amount of energy needed to raise the temperature of a substance by a unit degree. In analyzing scenarios where heat is added to an object, knowing its specific heat helps determine the resultant temperature change by relating the energy input to the change in internal energy.

Gravitational Potential Energy

Gravitational potential energy is the energy stored due to an object’s position in a gravitational field. When an object is raised or moves in a gravitational field, some of the supplied energy is used to increase this potential energy rather than solely increasing the internal energy (temperature), which affects the overall thermal outcome.

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