# Comparison of Heat and Work

Some of the similarities between heat and work are described under.

1. Heat and work are both transient phenomena. Systems never possess heat or work, but either or both cross the system boundary when a system undergoes a change of state.
2. Both heat and work are boundary phenomena. Both are observed only at the boundary of the system and both represents the energy crossing the boundary.
3. Both heat and work are path functions and inexact differential equations.

In sign convention, ‘+Q’ represents ‘Q’ amount of heat transferred to the system and thus is energy added to the system and ‘+W’ represents ‘W’ amount of work done by the system and thus is energy leaving the system.

Figure 1 (a) & (b) illustration explains the difference between heat and work, In the above Fig. a gas contained in a rigid vessel. Resistance coils are wound around the outside of the vessel. When current flows through the resistance coils, the temperature of the gas increases.

In Figure 1 (a), we consider only the gas as the system. The energy crosses the boundary of the system because the temperature of the walls is higher than the temperature of the gas. Therefore, we recognize that heat crosses the boundary of the system.

In Figure 1 (b), the system shows the vessel and the resistance heater. Electricity crosses the boundary of the system, as indicated earlier, this is work. Figure 2: The effects of heat addition to a control volume that also can give out work.

In Figure 2, a cylinder is fitted with a movable piston. There is a positive heat transfer to the gas, which tends to increase the temperature. It also tends to increase the gas pressure inside the piston. However, the amount of pressure changes by the amount of external force acting on its movable boundary. If pressure remains constant, then the volume increases instead. There is also the opposite tendency for a negative heat transfer, that is, one out of the gas. Consider again the positive heat transfer, except that in this case the external force simultaneously decreases. This causes the gas pressure to decrease so that the temperature tends to go down. In this case, there is a simultaneous tendency toward temperature change in the opposite direction, which effectively decouples the directions of heat transfer and temperature change.

Often when we want to evaluate a finite amount of energy transferred as either work or heat, we must integrate the instantaneous rate over time: In order to perform the integration, we must know how the rate of work and heat amount varies with time. For period of time when the rate of work does not change much. A simple average may be sufficiently accurate to allow us to write the equation which is similar to the information given on electric utility bill in kW-hours.