Summary 2: Transferring Energy, Heat and Work

System and Surroundings

Figure 1: A simple energy balance diagram

An energy balance tracks energy entering, leaving and accumulating in a system.

What is the system?

Figure 2: The system and surroundings defines where the energy balance is applied

The system is the part that we are interested in studying. The surroundings are everything else.

Often can freely choose the system-surroundings boundary location. Choosing well can simplify calculations.

System example 1

Figure 3: A stirred tank feed by a pump

The system could be:

  • the stirred tank
  • the pump
  • the pump + stirred tank

System example 2

Figure 4: A heat exchanger

The system could be:

  • the entire heat exchanger
  • the hot side of the heat exchanger
  • the cold side of the heat exchanger

How systems store energy

A system can store energy in three ways:

  • Potential Energy, \(E_p\)
  • Kinetic Energy, \(E_k\)
  • Internal Energy, \(U\)

Key Term

Internal Energy (\(U\)) — a thermodynamic state function describing the energy stored within matter.

How systems gain or lose energy

  • Heat, \(Q\)
    • Energy transferred to/from surroundings due to a temperature difference.
  • Work, \(W\)
    • Energy transferred to/from surroundings due to a force acting through a distance.
  • Mass flow, \(\dot{m}\)
    • Internal energy carried by mass entering or leaving the system.

Energy Balance Diagram

\[\text{Accumulation of Energy} = \text{Energy In} - \text{Energy Out}\]

\[\frac{dE_{sys}}{dt} = \dot{E}_{in} + \dot{Q} + \dot{W} - \dot{E}_{out}\]

Heat and Work convention

Important

Heat and work are defined as energy transfer into the system. If heat or work leaves the system, their values are negative.

Heat and work are quantities, not properties

Internal energy (\(U\)) is a property of the system.

Heat (\(Q\)) and work (\(W\)) are not properties of the system.

Important

Heat and work represent quantities of energy transfer. Heat is not stored in a system, and work is not stored in a system. When heat or work is transferred across the system boundary, the energy transferred is stored as \(U\), \(E_k\), or \(E_p\).

Heat and work are different

Heat and work are different forms of energy transfer.

  • Adding 100 J of heat to a system vs adding 100 J of work on a system.
  • Both will increase the energy of the system by 100 J
  • But the way energy is stored in the system may differ
  • Work is always more useful that heat

Example 2.1: Energy accumulation

A tank contains 500 L of toluene at 80 °C. The tank is cooled to 50 °C before half the toluene is withdrawn. The energy of the toluene scales with temperature by approximately 155 J/molK (this is the heat capacity). Calculate the energy accumulated in the tank relative to its initial state. The density of toluene is 0.867 kg/L and the molar mass is 92.14 g/mol.