# Tag Info

### Hamiltonian as a quadratic function

$$H= \sum_j A_j P_j^2 + \sum_j B_j Q_j^2$$ For such a system, "we clearly have" $$\sum_j \left( P_j \frac{\partial H}{\partial P_j}+ Q_j \frac{\partial H}{\partial Q_j}\right) = 2H.$$ ...

### Availability of system with constant pressure and temperature

But, dG = dU - d(ST) + d(pV)= Vdp - SdT If p and T is constant, dG is always zero... What's wrong in my reasoning? $$dG = dU - d(ST) + d(pV) = VdP - SdT + \mu dN\;,$$ where $\mu$ is the chemical ...

### Why does increasing the volume in which a gas can move increase its entropy?

The formula $dS=\frac{dQ}{T}$ can only be used when the process is reversible. In fact many text books adopt the notation $dQ_{\text{rev}}$. The process described in this question is not quasi-static ...

### What is an good book to study classical non-equilibrum thermodynamics?

So, if by classical you mean phenomenological, that is anything non-statistical, then I would suggest the general review book Lavenda: Thermodynamics of irreversible processes, see here, in which each ...
Accepted

### How do I calculate the Relative Humidity from number density and pressure?

Dividing the number density by avagadro's number gives you the number of moles per unit volume of water $\rho_w$. The partial pressure of water vapor is then $$P_{water}=RT\rho_{w}$$If, at ...

### How do I calculate the Relative Humidity from number density and pressure?

It appears to (non-expert) me that in the world our air is a very complex thing. It contains not only gases and water but a lot of biological materials such as bacteria, spores, dust... There are ...
Accepted

### Fluctuations of the center of mass of a confined fluid?

At equilibrium, if you believe Gibbs statistical mechanics, you expect the velocities to be uncorrelated since the kinetic part of the hamiltonian is just the sum of the kinetic energies of your ...

### What is the difference between enthalpy and internal energy?

As noted correctly above, enthalpy is just the sum of the internal energy and $PV$, \begin{gather*} H = E+PV \end{gather*} More formally, it is a Legendre transform of the internal energy that gives a ...

### Can any irreversible work source be simulated by a reversible work source?

It briefly explains the reason; what the work source does is simply to apply force to the piston, and therefore it does not matter how the force is applied, whether or not it is applied by an ...
Accepted

### Evaluating Maxwell Relations with Constant Entropy for Arbitrary EOS

$$dS=\frac{C_V}{T}dT+\left(\frac{\partial S}{\partial V}\right)_TdV=\frac{C_V}{T}dT+\left(\frac{\partial P}{\partial T}\right)_VdV$$ Also, dS=\frac{C_P}{T}dT+\left(\frac{\partial S}{\partial P}\...

### Evaluating Maxwell Relations with Constant Entropy for Arbitrary EOS

The state of a thermodynamic system is uniquely defined by (usually) 2 variables which can be any of the properties of the system, i.e. $p,V,T,S$, etc. Consequently the properties of the system, which ...
Accepted

### How does the excess GPE of a mountain cause its base to melt?

However, does there exist a physical explanation of how this occurs, not just one based on the conservation of energy From Weisskopf's response to comments: I have used the melting heat...as a ...
Accepted

### How to derive the Clausius Inequality?

The inequality for irreversible cycles follows from Carnot's theorem which states that no cyclic process can be more efficient than a Carnot cycle. The basic idea for deriving the equality for ...

### How to derive the Clausius Inequality?

How do we get here, to the Clausius inequality for any cycle? The Clausius inequality applies to any heat engine cycle, where $T$ is the temperature at the point of heat entry but which, unlike the ...
Accepted

Brian Bi gave a good physical example of a situation where the equality $\sum_j v_j\mu_j = 0$ does not hold. I want to discuss the issue from a more formal point of view. The equality $\sum_j v_j\mu_j ... 3 votes ### Why is$\sum\limits_j {{v_j}{\mu _j}} = 0\$ sometimes can't be achieved?

The best known example is when a solid dissolves in water (though it can be any liquid, really): we model this as the reaction X(s) -> X(aq). If there is a sufficiently large amount of water ...

### How to derive the Clausius Inequality?

Personally, I find the Clausius inequality easiest to think of without considering cycles at all. Thermodynamic processes obey a succinct relationship between the reversible and irreversible work done ...