The first law of thermodynamics states that heat and work are?

The first law of thermodynamics is fundamentally about the conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another. This implies that heat and work, both forms of energy transfer, are indeed mutually convertible.

In practical terms, this means that the energy transferred as heat can be converted into work when a system undergoes a change (like in a heat engine), and vice versa. For instance, by manipulating the temperature of a gas, you can either extract work from it or add heat to it, showing the interchangeability of these two forms of energy.

The other options, while they might seem plausible, do not accurately reflect the principle outlined in the first law. Heat and work being “not convertible” or “sometimes convertible” contradicts the law's assertion of energy transformation, while “mutually fusible” misrepresents the nature of energy interactions. Therefore, it is clear that option that states they are mutually convertible aligns perfectly with the established principles of thermodynamics.