Which physicist is known to establish the relationship between mechanical work and heat transfer?

The correct answer is James Prescott Joule.

James Prescott Joule (1818–1889) was a British physicist who conducted a series of groundbreaking experiments in the mid-19th century that firmly established the quantitative relationship between mechanical work and heat transfer. His work laid the foundation for the First Law of Thermodynamics — the law of conservation of energy.

What did Joule discover?

Joule demonstrated that heat is not a separate fluid (as was previously thought under the "caloric theory") but rather a form of energy. He showed that a specific, measurable amount of mechanical work always produces a specific, equivalent amount of heat. This fixed ratio is called the mechanical equivalent of heat.

Joule's Famous Paddle-Wheel Experiment:
In his most celebrated experiment, Joule set up a system where falling weights turned a paddle wheel submerged in water. The key observations were:

• The falling weights did mechanical work on the paddle wheel.
• The spinning paddle wheel agitated the water, generating friction.
• This friction caused a measurable rise in the temperature of the water.
• By carefully measuring the work done (via the weight and height of fall) and the heat produced (via the temperature rise), Joule calculated a precise conversion factor.

The Result — Mechanical Equivalent of Heat:

Joule found that approximately 4.18 Joules of mechanical work produces 1 calorie of heat. In modern notation:

1\text{calorie}=4.186\text{Joules}

This relationship can be expressed through the First Law of Thermodynamics:

Q=W

where Q is the heat energy and W is the mechanical work done — confirming their equivalence.

Why not the other options?

• William Henry — Known for Henry's Law, which describes the solubility of gases in liquids. Not related to heat and work.
• Hermann Helmholtz — Made important contributions to the general principle of conservation of energy, but it was Joule's experimental work that specifically quantified the mechanical-heat relationship.
• John Dalton — Known for his Atomic Theory of matter and Dalton's Law of partial pressures. Not directly associated with mechanical work and heat.

Legacy:
In honor of his immense contributions, the SI unit of energy is named the Joule (J), which is used universally today in all branches of science and engineering to measure work, heat, and energy.