In a closed system, no mass may be transferred in or out of the system boundaries. The system will always contain the same amount of matter, but heat and work can be exchanged across the boundary of the system. Whether a system can exchange heat, work, or both is dependent on the property of it boundary.
- Adiabatic boundary – not allowing any heat exchange
- Rigid boundary – not allowing exchange of work
One example is fluid being compressed by a piston in a cylinder. Another example of a closed system is a bomb calorimeter, a type of constant-volume calorimeter used in measuring the heat of combustion of a particular reaction. Electrical energy travels across the boundary to produce a spark between the electrodes and initiates combustion. Heat transfer occurs across the boundary after combustion but no mass transfer takes place either way.
Beginning with the first law of thermodynamics for an open system, this is expressed as:
where U is internal energy, Q is heat transfer, W is work, and since no mass is transferred in or out of the system, both expressions involving mass flow, , zeroes, and the first law of thermodynamics for a closed system is derived. The first law of thermodynamics for a closed system states that the amount of internal energy within the system equals the difference between the amount of heat added to or extracted from the system and the wok done by or to the system. The first law for closed systems is stated by:
- dU = δQ − δW
where U is the average internal energy within the system, Q is the heat added to or extracted from the system and W is the work done by or to the system.
Substituting the amount of work needed to accomplish a reversible process, which is stated by:
- δW = PdV
where P is the measured pressure and V is the volume, and the heat required to accomplish a reversible process stated by the second law of thermodynamics, the universal principle of entropy, stated by:
- δQ = TdS
where T is the absolute temperature and S is the entropy of the system, derives the fundamental thermodynamic relationship used to compute changes in internal energy, which is expressed as:
- δU = TdS + PdV
The second law of thermodynamics is only true for closed systems. It states that the entropy of an isolated system not in equilibrium will tend to increase over time, approaching maximum value at equilibrium. Overall, in a closed system, the available energy can never increase, and it complement, entropy, can never decrease.
An isolated system is a type of closed system that does not interact with its surroundings in any way. Mass and energy remains constant within the system, and no energy or mass transfer takes place across the boundary.
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