All Questions
33 questions
3
votes
2
answers
115
views
Pressure of mixture after mixing [closed]
An insulated rigid tank is divided into two compartments by a partition. One compartment contains $3 \,\text{kmol}$ of $\mathrm{O}_2$, and the other compartment contains $5 \,\text{kmol}$ of $\mathrm{...
- 31
5
votes
5
answers
2k
views
What happens to entropy during compression?
I learnt that entropy in the universe can only be created, never destroyed. (And so change in entropy can never be negative, right?)
But during compression, don't we increase the order in, say, the ...
- 1,096
1
vote
2
answers
140
views
Definition of the pressure in statistical mechanics
I just had a glimpse of Feynman's statistical mechanics. On page 8, I saw a 'third' definition of pressure:
$$ P = - \frac{\partial U }{\partial V} (V, S) . $$
I am curious why it is $S$ but not $T$. ...
- 2,165
0
votes
0
answers
37
views
Entropy of mixing via partial pressures
I was deriving the equations for calculating the entropy change $\Delta S_M$ of the system where ideal gases are being mixed.
The first one utilizes partial pressures via Dalton's law:
$$\Delta S_M= \...
- 904
-1
votes
1
answer
57
views
How is entropy calculated in a Constant Temperature process, when a gas is compressed from from $p_1$ to $p_2$? [closed]
Entropy for constant temperature process, when instead of volumes, pressures changes from $p_1$ to $p_2$?
0
votes
1
answer
58
views
Find the ideal gas law from the internal energy [closed]
I'm looking for a way on how to obtain the ideal gas law $PV=nRT$ by being given the internal energy $$U=U(S,V)=\alpha N k_b \left(\frac NV\right)^{2/3} e^{2S/(3Nk_b)}$$ I can find the pressure and ...
- 69
0
votes
2
answers
147
views
Enthalpy of a Van der Waals gas continuation
In my previous question Enthalpy of a Van der Waals gas, I got the expression of the enthalpy generalised, but I am still having issues finishing it since it might have some quite hard calculus...
For ...
- 69
0
votes
2
answers
150
views
Entropy Departure - BWRS Equation of State [closed]
Edit: This was not a homework problem. I simply pulled an example from a textbook to easily illustrate and convey the problem at hand.
I am seeking some assistance in evaluating the entropy change of ...
0
votes
2
answers
257
views
Entropy change for a real gas via Peng-Robinsons EOS
Consider a process with inlet conditions ~300K,~50Bar and outlet conditions ~350K,~150Bar. Entropy departures as per Peng-Robinsons EOS. I am evaluating the entropy change via the following:
∆𝐒 = 𝑺𝒅...
0
votes
1
answer
87
views
Intuition behind entropy and its differentiation
I was reading the following paper about a better intuition of entropy and how it is connected to heat energy without the use of microstates:
The problem is when he assumed that volume is constant and ...
1
vote
1
answer
68
views
Slope of constant pressure line on $T$-$S$ plot
Is slope of constant pressure line is same or di in liquid region and super heated region for pure substance on $T$-$S$ diagram?
- 51
0
votes
1
answer
111
views
Entropy for constant pressure
Is it valid to say that at constant pressure the entropy can be written as follows
$$S=\left(\frac{\partial U}{\partial T}\right)_{p}~?$$
0
votes
2
answers
224
views
Why doesn't the formula for the entropy change of an isobaric process include a work term?
I tried to derive the entropy change of an isobaric process and arrived at:
$\Delta S = C_pln(T_2/T_1)+nRln(V_2/V_1)$
However, it appears the answer is just:
$\Delta S = C_pln(T_2/T_1)$
It seems like ...
0
votes
2
answers
315
views
Thermodynamic equilibrium state of constant $(p,S)$ system
The internal energy as a function of its natural variables is:
$$dU=-p dV+TdS$$
where $p$ is the system pressure and $dS$ includes only changes of the entropy due to heat transfer (the "...
- 474
6
votes
4
answers
1k
views
The definition of Spontaneous in thermodynamics?
The definition of spontaneous is often briefly glossed over in most of the thermodynamics texts that I own. Peter Atkins in Physical chemistry defines spontaneous as follows
Some things happen ...
- 1,599
1
vote
3
answers
605
views
More reversible heat required to do the same work as an irreversible process?
Suppose we have the reversible isothermal process from state a to b as shown below:
The work done by the system is simply equal to the area under the curve. The fact that this process is isothermal ...
- 1,599
0
votes
2
answers
810
views
Thermodynamics and the state postulate: should it be a Fourth Law?
The state postulate is as follows: The state of a simple compressible system is completely specified by two independent, intensive properties.
My first question is whether there is any justification ...
- 1,599
1
vote
2
answers
125
views
How do I properly partially differentiate with constant $p$ in thermodynamics?
I'm trying to solve the following problem:
a one component system is described by the following equations
$$U=\frac{A^2}{4}NT^2\exp \left(\frac{V^2}{N^2}\right),\qquad p=T^2f(v)$$
where $v = \frac{V}{...
0
votes
2
answers
213
views
Calculate Entropy from pressure and energy
It's given that for a particular special gas, the pressure and the energy is given by,
$
\begin{aligned}
P &=\left(\sqrt{\frac{N}{V}}\right) \frac{T^{2}}{A} \\
E &=2 \sqrt{N V} \frac{T^{2}}{A}
...
- 137
1
vote
1
answer
972
views
Pressure, entropy and enthalpy
For an ideal compressible flow, this relation holds:
$$P = P(s, h)$$
where $s$ is the specific entropy and $h$ is the specific enthalpy.
I don't know why: I know that $s = s(e, v)$, but even using ...
- 35
0
votes
1
answer
92
views
Why is $c_{p,avg}$ used in a process that involves the change of pressure?
There is an example of exercise in a book "Thermodynamics, An Engineering Approach, the 8th edition" by Yunus A. Cengel and Michael A. Boles (example 7-9) stating that:
Air is compressed from an ...
- 41
1
vote
0
answers
132
views
Can you plot irreversible but quasi static processes on a $pV$ diagram?
I've often heard that you can't plot irreversible processes on a $pV$ diagram, but what about in the case where you have a quasi static process with friction? There still exists a curve of ...
- 2,654
0
votes
1
answer
49
views
Does concentration gradient or difference in number of particles affect pressure?
Suppose I have 2 identical boxes and both of them are divided into 2 equal halves by a board. Now I fill the 2 boxes with different total number of air particles, and with different number of air ...
0
votes
3
answers
698
views
How does a bottle filled with fluid which has been vigorously shaken, lose entropy to the surroundings?
Suppose a bottle is filled with a hypothetical liquid that cannot absorb air/gas. The cap is tightened enough to prevent any loss or gain of mass. Now, this bottle is vigorously shaken and then ...
- 66
1
vote
0
answers
206
views
Why are diamonds formed under high pressure? (use entropy)
My book asks how can diamond ever be more stable than graphite, when it has less entropy. I have to explain how at high pressures the conversion of graphite to diamond can increase the total entropy ...
- 992
0
votes
1
answer
917
views
Entropy variation over a thermodynamic cycle
How to calculate the entropy variation of a thermodynamics cycle that looks like a circle? The cycle is the same as in this photo
2
votes
1
answer
2k
views
Deriving $Tds$ relations in thermodynamics
The Tds relations I refer to are, $$Tds = du + Pdv$$$$Tds = dh - vdP$$
The first equation is derived (assuming internally reversible process) from the definition of entropy $ds = \delta Q/T$ and the ...
- 321
2
votes
1
answer
196
views
Does entropy really not increase here?
Two vessels separated by a partition have equal volume $V_0$ and equal temperature $T_0$. They both contain the same ideal gas, and the particles are indistinguishable. The left vessel has pressure $...
- 5,421
4
votes
3
answers
21k
views
What is the relation between entropy and pressure in strict thermodynamic terms?
I read on the net that it is a general consensus that entropy in a system decreases as pressure increases and vice versa.
How can one reach such conclusion using the characteristic equation in terms ...
- 143
0
votes
4
answers
8k
views
Does the entropy of an adiabatically isolated system stays the same after we decrease/increase the pressure?
Even if the system is isolated and there is no heat exchange with surroundings, shouldn't the decrease/increase of pressure result in increase/decrease of entropy?
Does this property of an ...
- 11
0
votes
0
answers
71
views
Which pressure to use in the $T~ds$ equation?
Let's say I have an adiabatic, rigid, open container that has an amount of air at some pressure, $P_\text{cv}$, and some temperature, $T_\text{cv}$. I have heated pressurized air coming into the ...
- 1,158
1
vote
0
answers
194
views
How to solve state parameters using these givens for an ideal gas?
In a thermodynamic turbine using air as an ideal gas, given that you have a known inlet temperature value $T_i$, a known exit pressure value $P_e$, a known inlet and exit velocity $V_i$ and $V_e$, a ...
- 1,511
1
vote
2
answers
4k
views
What is the physical or mathematical meaning of the Gibbs-Duhem equation?
The Gibbs-Duhem equation states
$$0~=~SdT-VdP+\sum(N_i d\mu_i),$$
where $\mu$ is the chemical potential. Does it have any mathematical (about intensive parameters) or physical meaning?
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