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asdf1
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When proving the equation,
dU=TdS-PdV
why is dw= PdV not dw= PdV +vdP?
dU=TdS-PdV
why is dw= PdV not dw= PdV +vdP?
Work (force x distance) is done only if the pressure (force/area) acts over some change in volume (area x distance moved). If there is no change in volume, the force does not act over any distance - ie. the pressure just builds up but does not move anything (ie. it just increases internal energy). So, VdP is part of the internal energy of the gas, not the work done by the gas.asdf1 said:When proving the equation,
dU=TdS-PdV
why is dw= PdV not dw= PdV +vdP?
This statement is known as the first law of thermodynamics, which states that the change in internal energy (dU) of a system is equal to the sum of the heat transfer (TdS) and work done (PdV) on the system. The second part of the statement, "dw=PdV Not dw=PdV+vdP", emphasizes that the work done by the system is only equal to PdV, not PdV+vdP as often assumed.
As stated in the first law of thermodynamics, dU is equal to the sum of TdS and PdV. This means that any change in internal energy is a result of changes in temperature (T), entropy (S), and volume (V) of the system.
The second part of the statement, dw=PdV Not dw=PdV+vdP, is important because it clarifies that the work done by a system is not equal to PdV+vdP. This is a common misconception and can lead to incorrect calculations.
The first law of thermodynamics, dU=TdS-PdV: dw=PdV Not dw=PdV+vdP, is used in many branches of science, including chemistry, physics, and engineering. For example, in chemical reactions, the change in internal energy of a system can be calculated using the heat transfer (TdS) and work done (PdV) on the system.
The first law of thermodynamics has many practical applications, such as in the design and operation of heat engines, refrigeration systems, and power plants. It is also used in fields such as meteorology, where it helps explain atmospheric phenomena such as the formation of clouds and the Earth's energy balance.