Work and Heat

Work is expressed as the dot product of force and displacement vectors, making it a scalar quantity measured in Joules. For a gas confined by a frictionless piston, work performed by the system against constant external pressure is calculated as dw = –pext dV, where the negative sign indicates energy decreases as the system expands.

When the piston moves outward, the gas expands and performs work on its surroundings, reducing internal energy. Conversely, when the piston moves inward, the surroundings perform work on the gas, compressing it and increasing internal energy. These changes directly relate to internal energy and formulation of the first law.

Total work is calculated by integrating infinitesimal volume changes. When external pressure remains constant, the integral simplifies to w = –pext(Vf – Vi), where Vf and Vi are final and initial volumes. For reversible processes, external pressure equals internal pressure, allowing calculation using the ideal gas law.

Heat is the transfer of thermal energy measured in joules or calories. Unlike work, which involves mechanical energy transfer, heat represents energy transfer due to temperature differences. Both work and heat influence a system's internal energy, but heat can be absorbed or released, changing the system's temperature.

Specific heat capacity (c), measured in J/g·K, is an intensive property that determines how much heat is needed to raise a substance's temperature. The heat required for a temperature change depends on the mass, temperature change, and specific heat capacity. This relationship quantifies the thermal energy transfer needed for a given temperature shift.

The negative sign in dw = –pext dV signifies that work contributes to a decrease in the system's energy when the system expands against external pressure. This sign convention ensures that expansion work is represented as negative, reflecting energy loss from the system to its surroundings during volume increase.

Work and heat are the two primary mechanisms through which internal energy changes. When a system absorbs heat, its internal energy increases; when it releases heat, internal energy decreases. Similarly, work done on the system increases internal energy, while work done by the system decreases it. Both quantities are path-dependent and interact to determine total energy change.