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How can internal energy be expressed as a function of any two of $p, v, T$?

In the book of Irey, Theormodynamics, the author states that (while talking about single phase substances) For a simple compressible media, we may choose our measurable independent variables any ...
0
votes
3answers
73 views

Sign of $(\partial T /\partial V )_E$

Consider a realistic gas. If it is insulated and then allowed to expand into a vacuum, how does its temperature change? We have to consider the sign of $\left(\dfrac{\partial T}{\partial V }\right)...
0
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2answers
46 views

Does the total energy in a volume (gas) increase linearly with increases in pressure?

If a volume has a certain pressure, then double that pressure at another time, is the total energy stored doubled? I'm sure this has to do with thermodynamics and if I remember correctly there is a ...
4
votes
3answers
220 views

Why is there Net Work Done on a Pressure/Volume Cycle?

The area enclosed by the rectangle is said to be the Net Work Done. My question is why would there be any net workdone if it returns to its initial position (W). Shouldn't it act like a force-...
0
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2answers
48 views

Change of specific internal energy due to temperature and volume

The change of internal energy due to temperature and volume may be written as $$ dU=C_V dT + \left( T\left(\frac{\partial S}{\partial V}\right)_T-P\right) dV$$ where $$\left(\frac{\partial S}{\partial ...
0
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2answers
37 views

$p$-$V$ diagram and internal energy

I recently learned that if the initial state is equal to the final state in the $p$-$V$ diagram then the internal energy is equal to zero so that means $Q=W$. My question is how can you know that only ...
0
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2answers
68 views

Isn't the equation of state for ideal gas valid in the free expansion?

I am deeply confused.... For a thermally insulated ideal gas expanding freely, I think that $PV^{\gamma}=cnst$ must hold. Through the equation $PV=nRT$, it must be that $TV^{{\gamma}-1}=\rm constant$. ...
0
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2answers
3k views

Deriving a thermodynamic relation using the Helmholtz free energy

I'm supposed to derive the following thermodynamic identity: $$ - \left( \frac{\partial U}{\partial V} \right)_{T,N} + T \left( \frac{\partial P}{\partial T} \right)_{V,N} = P $$ ...by starting with ...
1
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1answer
330 views

Thermodynamics - internal energy

What would the curve that describes the change of internal energy ($U$) with the volume ($V$) be like if the change in the temperature is negative? My try: For a ideal monoatomic gas, we have $U=(3/...
-5
votes
1answer
166 views

Does thermal energy change within a chamber depending on what's in it, where it is, what it is?

I have noticed that some people will say that, when you put more mass in an oven, it takes longer for both to cook than if just were one. Some others will say that timings are the same. Assume we ...
1
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3answers
4k views

How is it possible to equate the internal energy at constant volume with the internal energy of an adiabatic process?

I hope my question makes sense. My problem is that, I have read through numerous textbooks that $$nCdT = -PdV$$ (where $NC$ is constant volume) when deriving the relationship between $T$ and $V$ for ...