Gibbs Free Energy () is a thermodynamic principle that tells us about only about the spontaneity of a reaction (whether or not the reaction will occur). On the other hand, the rate of a reaction can be described by chemical kinetics. The question gives no information about the kinetics of the reaction, and we therefore cannot draw any conclusions about the rates of the two reactions described.

The Gibbs Free Energy ()of a reaction tells us whether or not the reaction is favorable. A favorable reaction is also known as spontaneous, and has a negative . A non-favorable reaction is non-spontaneous, and has a positive . The term exergonic (meaning energy exits the system) is also used for a reaction with a negative , while the term endergonic (meaning energy enters the system) is used for a reaction with a positive . Therefore, a reaction with is both exergonic and spontaneous.

The correct answer is "metabolism in brown fat cells." The mitochondria in brown fat have a protein called thermogenin that acts as a proton channel, which allows the dissipation of the proton gradient made by the electron transport chain. This allows oxidative phosphorylation to continue, and produce heat, without the production of ATP. Answers a and b, which both involve ATP hydrolysis, are also used by humans to produce heat but do not involve the uncoupling of oxidative phosphorylation from ATP production. Sweating and vasodilation of blood vessels are both ways that the human body loses heat.

The spontaneity of a reaction says nothing about the reaction's speed. For a spontaneous reaction, the change in Gibbs free energy is negative. In other words, the products have lower energy than the reactants. With low temperatures and negative enthalpy, a reaction can still proceed spontaneously if entropy decreases.