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Prathyush
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Is work done by the external agency when an adiabatic change in the Hamiltonian is performed on some State ψ?
An adiabatic change refers to a thermodynamic process in which there is no transfer of heat between the system and its surroundings. This means that the change in internal energy of the system is solely due to work done on or by the system.
In an adiabatic change, work is the only means by which the internal energy of the system can be changed. This can be either work done on the system, resulting in an increase in internal energy, or work done by the system, resulting in a decrease in internal energy.
The formula for calculating work in an adiabatic process is W = -PΔV, where W is work, P is pressure, and ΔV is the change in volume of the system. This formula is based on the first law of thermodynamics, which states that the change in internal energy of a closed system is equal to the sum of heat and work.
Yes, an adiabatic change can result in a change in temperature. This is because the change in internal energy of the system is related to the change in temperature through the specific heat capacity of the substance. Therefore, work done on or by the system can cause a change in temperature, even in the absence of heat transfer.
An adiabatic change is different from an isothermal change in that an adiabatic change does not allow for any heat transfer between the system and its surroundings, while an isothermal change occurs at a constant temperature and allows for heat transfer. Additionally, in an adiabatic change, the change in temperature is not constant, while in an isothermal change, the change in temperature is zero.