The objective is the average gas pressure P . Consider the canonical ensemble for a volume of ideal gas.
T enters via the canonical statistical weight , because .
The pressure is the force which the gas exerts on the walls of its container. The force exerted on the wall by a single atom is , being the unit vector normal to the wall. The atoms cannot pass beyond the walls, so as , and similarly for the other walls. The pressure P depends on the exact position of the gas atoms, so P varies from element to element of the canonical ensemble. Similarly, in a real system P fluctuates in time, changing as the gas molecules move within their container.