Two pieces of metal (A and B) are identical in every way, except that A has a much larger thermal expansion coefficient. If equal amounts of heat are added to both pieces of metal, which metal does more work on its surroundings?

To determine which metal does more work on its surroundings, we need to understand the concept of work done by a substance during thermal expansion.

When a substance undergoes thermal expansion, it expands and exerts a force on its surroundings. This force, combined with the displacement of the substance, constitutes the work done by the substance on its surroundings.

The equation for the work done is given by:

Work = Force × Displacement × cos(θ)

Where:
- Force is the magnitude of the force exerted by the substance during expansion.
- Displacement is the distance over which the expansion occurs.
- θ is the angle between the force and the displacement vectors. In the case of thermal expansion, θ is generally 0°, as the force and displacement act in the same direction.

Now, let's consider the two pieces of metal, A and B. Metal A has a much larger thermal expansion coefficient, which means it will expand more when the same amount of heat is added compared to metal B. Consequently, metal A will exert a larger force on its surroundings during expansion compared to metal B.

Assuming the displacement is the same for both metals, the equation for work done implies that the work done by metal A on its surroundings will be greater than the work done by metal B.

In summary, when equal amounts of heat are added to both pieces of metal, metal A, with the larger thermal expansion coefficient, will do more work on its surroundings due to its greater expansion and the resulting larger force it exerts.