Work and Heat

Work and heat are fundamental concepts in thermodynamics, denoting the transfer of energy. Work is the energy transferred due to the movement of an object under force, represented as the dot product of the force and displacement vectors. An example can be seen in a gas confined by a frictionless piston. The gas performs work on its surroundings when the piston moves outward, reducing the system's energy.

This infinitesimal amount of work (dw) performed by the system against a constant external pressure (p_ext) during an infinitesimal change in volume (dV) is defined as dw = –p_ext dV. The negative sign signifies that the work contributes to a decrease in the system's energy. Conversely, when the piston moves inward, the surroundings perform work on the system, increasing its energy. The total work done on or by the system can be calculated by integrating all the infinitesimal changes contributing to an overall change. If the external pressure remains constant throughout the process, the integral simplifies to w = –p_ext(V_f – V_i), where V_f and V_i are the final and initial volumes, respectively. For reversible processes, the external pressure equals the internal pressure. For such reversible changes, the work can be calculated using the ideal gas law.

Heat signifies the transfer of thermal energy. Heat can either be absorbed or released by a system, thus increasing or decreasing its temperature, respectively.

The required heat for a temperature change is proportional to the temperature shift and the system's mass; this relationship is quantified by the specific heat capacity.