20.8
Cyclic Processes And Isolated Systems
A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of…
A system that does not exchange heat and does no work on its surroundings is called an isolated system. The change in internal energy for such systems is zero.
In non-isolated systems, the internal energy can be constant only if the process followed is cyclic.
Suppose a thermodynamic system, like air inside the lungs, at initial pressure and volume, expanded to a new final state, returns to its initial state in a thermodynamic process. Such a process is called a cyclic process.
In this process, the internal energy of the gas remains constant; therefore, the work done equals the net heat transfer.
In a pV diagram, such a cyclic process is represented by a closed path. Suppose the work done along the first path is W1, and work done along the second path is W2. The net work done in a cyclic process is represented by the area between these two closed paths.
It is positive if the process follows a clockwise cycle and is negative when it follows a counter-clockwise cycle.
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Q1: What is an isolated system in thermodynamics?
An isolated system is a thermodynamic system that does not exchange heat with its surroundings and performs no work on them. For isolated systems, the change in internal energy is always zero because no energy enters or leaves the system. This principle is fundamental to understanding energy conservation in thermodynamic processes.
Q2: Why does internal energy remain constant in a cyclic process?
In a cyclic process, a system returns to its initial state after undergoing a series of changes. Since internal energy is a state function depending only on initial and final states, returning to the initial state means internal energy returns to its original value, making the net change zero. Therefore, the net work done equals the net heat transfer in the cycle.
Q3: How is net work represented in a cyclic process on a pV diagram?
On a pV diagram, a cyclic process is represented by a closed path. The net work done equals the area enclosed within this closed path. If the cycle follows a clockwise direction, the net work is positive; if counter-clockwise, the net work is negative. This graphical representation helps visualize energy transformations during the complete cycle.
Q4: What is the relationship between heat transfer and work in a cyclic process?
In a cyclic process, since internal energy change is zero, the net work done by the system equals the net heat transfer into the system. If the net heat transfer is positive, the system does positive work on surroundings. If negative, work is done on the system. This relationship directly follows from the first law of thermodynamics applied to cyclic processes.
Q5: How do you calculate net work done in a multi-step cyclic process?
To find net work in a multi-step cyclic process, first calculate the total heat transfer by summing heat values for each step. Since internal energy change is zero in a cyclic process, the net work done equals this total heat transfer. For example, if individual heat transfers are 40 J, −80 J, −20 J, and 100 J, the net work is their sum: 40 J.
Q6: What does positive net work indicate in a cyclic thermodynamic process?
Positive net work in a cyclic process means the system does more work on its surroundings than work done on the system. This occurs when the cycle follows a clockwise path on a pV diagram. The heat energy supplied to the system is converted into external work, making the process useful for energy conversion applications like heat engines.
Q7: How do isolated systems and cyclic processes relate to internal energy?
Both isolated systems and cyclic processes maintain constant internal energy. An isolated system has zero internal energy change because it exchanges no heat or work. A cyclic process in a non-isolated system also has zero internal energy change because it returns to its initial state. Both demonstrate that internal energy depends only on the system's state, not the path taken.