Mathematical Expression Of First Law

Let UA be the energy of a system in its state A and UB be the energy in its state B. Suppose the system while undergoing change from state A to state B absorbs heat q from the surroundings and also performs some work (mechanical or electrical), equal to w. The absorption of heat by the system tends to raise the energy of the system. The performance of work by the system, on the other hand, tends to lower the energy of the system because performance of work requires expenditure of energy. Hence the change of internal energy, ΔU, accompanying the above process will be given by

ΔU = U _B - U _A = q - w

In general, if in a given process the quantity of heat transferred from the surrounding to the system is q and work done in the process is w, then the change in internal energy,

ΔU = q + w

This is the mathematical statement of the first law of thermodynamics.

If work is done by the surroundings on the system (as during the compression of a gas), w is taken as positive so that ΔU = q + w. if however work is done by the system on the surroundings (as during the expansion of a gas), w is taken as negative so that ΔU = q – w.

Related Topics

• Hess's Law
• Gibbs Free Energy