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Your problem is that much of the terminology of thermodynamics was defined before the underlying physical concepts were properly understood, which leaves us stuck with a lot of confusing names for things now. In particular, you're worried about the applicability of the quantity commonly known as the "specific heat capacity at constant volume". The ...

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The word "convert" is reserved for units that measure the same quantity (like distance in inches or cm). In this case however you need to use the word "calculate" because the units are dissimilar. Yes, the Darcy's Law equation is what you are looking for. In SI units, permeability "k" is measured in m2. In SI units, porous ...

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The fundamental relation for any closed system can be written as $$dU=\left(\frac{PC_V}{T\alpha K}\right)dT+\left(T-\frac{P}{\alpha K}\right)dS,$$ where $U$ is energy, $P$ is pressure, $C_V$ is the constant-volume heat capacity, $T$ is temperature, $\alpha$ is the thermal expansion coefficient, $K$ is the bulk modulus, and $S$ is entropy. If heating is ...

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Start with the first law. $$dU = \delta q + \delta w$$ Isentropic sets $dS = \delta q /T = 0$, giving $dU = \delta w$. For an ideal gas with a constant specific heat, $dU = C_v dT$. This gives the equation being used. $$\Delta U = C_v \Delta T = w$$ If temperature decreases, work is negative, meaning it is done by the gas. Alternatively, if temperature ...

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