Thermodynamics

Work is defined in mechanics in terms of force acting over a distance; that definition is exactly the same in thermodynamics. This is best illustrated by calculating the work done by a force F in compressing a volume of gas. If a volume of gas V is contained in a cylinder at pressure P, the force needed on the piston is (by the definition of pressure) equal to PA, where A is the area of the piston. Let the gas now be compressed in a manner which keeps the pressure constant (by letting heat flow out, so that the temperature also decreases); suppose the piston moves a distance d. Then the work done is W = Fd = PAd. But Ad is the amount that the volume has decreased, V_i - V_f, where V_i is the initial volume and V_f is the final volume. (Note that this volume difference gives a positive value for the distance, in keeping with the fact that work done on a gas is taken as positive.) Therefore, the work done on a gas during a compression at constant pressure is P(V_i - V_f).

The first law thus gives a straightforward means to determine changes in the internal energy of an object (and it is only changes in the internal energy that can be measured), since the change in internal energy is just equal to the work done on the object in the absence of any heat flow. Heat flow to or from the object can be minimized by using insulating materials, such as fiberglass or, even better, styrofoam. The idealized process where there is zero heat flow is called an adiabatic process.