Is there a clear analogy here between volume and entropy? Looking at: $\frac{dQ}{T}=dS,\frac{dW}{P}=dV$

Bernard Boyer
2022-07-20
Answered

Is there a clear analogy here between volume and entropy? Looking at: $\frac{dQ}{T}=dS,\frac{dW}{P}=dV$

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minotaurafe

Answered 2022-07-21
Author has **22** answers

The general expression for the first law (using the OP sign convention) is: $dE=\delta q+\delta w$. When the process is reversible it is possible to write: $dE=TdS+PdV$. This expression is the diferential of a function E(S,V):

$dE=\frac{\mathrm{\partial}E}{\mathrm{\partial}S}dS+\frac{\mathrm{\partial}E}{\mathrm{\partial}V}dV$

The similarity between V and S in the expression is that both are independent functions of the internal energy, while temperature and pressure are partial derivatives:

$T=\frac{\mathrm{\partial}E}{\mathrm{\partial}S}$

$P=\frac{\mathrm{\partial}E}{\mathrm{\partial}V}$

$dE=\frac{\mathrm{\partial}E}{\mathrm{\partial}S}dS+\frac{\mathrm{\partial}E}{\mathrm{\partial}V}dV$

The similarity between V and S in the expression is that both are independent functions of the internal energy, while temperature and pressure are partial derivatives:

$T=\frac{\mathrm{\partial}E}{\mathrm{\partial}S}$

$P=\frac{\mathrm{\partial}E}{\mathrm{\partial}V}$

asked 2022-05-17

Which among the following is the formula for Helmholtz free energy?

a) U+TS

b) U+TV

c) U-TS

d) UTV

a) U+TS

b) U+TV

c) U-TS

d) UTV

asked 2022-05-13

Heat transfer vs calorimetry equation

I'm trying to understand the difference between the equations

$Q=mc\mathrm{\Delta}T$

and,

$\frac{dQ}{dt}=\frac{-\kappa \alpha \mathrm{\Delta}T}{l}$

Suppose, we have two metal rods at ${T}_{1}$ and ${T}_{2}$ temperature, and we connect them at the end. I want to know, what do the two above equations tell us, regarding this system.

My understanding is that the first equation tells us, that the two systems will reach an equilibrium temperature, and the heat gained by one rod would be the heat lost by the other. This final temperature would depend upon the relative masses, and heat capacities. However, the first equation tells us, how much heat flows out of the first rod, into the second rod, and the final temperature.

Where does this second equation come from, and what does it tell us ? It seems to me, that the second equation would give us the heat transferred from one rod to the other, in some given time, unlike the first one that gives us the total heat transferred.

Combining the two above equations, we can derive the partial differential equation, called the heat equation. My question is, what does my heat equation tell me ? The first equation tells me, the final temperature of two bodies in contact, provided I know the initial temperature, mass and heal capacities.

What does the heat/diffusion equation tell me then ? Does it tell me, the distribution of heat at some given time ?

Does it mean, if I use the heat equation for our problem with the two rods at different temperatures, I'd get the same final temperature as the $Q=mc\mathrm{\Delta}T$ equation, after some time, and this temperature would be constant ?

I'm trying to understand the difference between the equations

$Q=mc\mathrm{\Delta}T$

and,

$\frac{dQ}{dt}=\frac{-\kappa \alpha \mathrm{\Delta}T}{l}$

Suppose, we have two metal rods at ${T}_{1}$ and ${T}_{2}$ temperature, and we connect them at the end. I want to know, what do the two above equations tell us, regarding this system.

My understanding is that the first equation tells us, that the two systems will reach an equilibrium temperature, and the heat gained by one rod would be the heat lost by the other. This final temperature would depend upon the relative masses, and heat capacities. However, the first equation tells us, how much heat flows out of the first rod, into the second rod, and the final temperature.

Where does this second equation come from, and what does it tell us ? It seems to me, that the second equation would give us the heat transferred from one rod to the other, in some given time, unlike the first one that gives us the total heat transferred.

Combining the two above equations, we can derive the partial differential equation, called the heat equation. My question is, what does my heat equation tell me ? The first equation tells me, the final temperature of two bodies in contact, provided I know the initial temperature, mass and heal capacities.

What does the heat/diffusion equation tell me then ? Does it tell me, the distribution of heat at some given time ?

Does it mean, if I use the heat equation for our problem with the two rods at different temperatures, I'd get the same final temperature as the $Q=mc\mathrm{\Delta}T$ equation, after some time, and this temperature would be constant ?

asked 2022-05-08

Answer the following True or False questions, explaining your reasoning in terms of the laws of thermodynamics where appropriate: (a) The quantities U, H, A, and G all have the same dimensions (i.e. expressed in the same units). (b) A(TS) = (AT)S+TAS. (c) The chemical potential µ¡ of a component i is a state function. d) The chemical potential of benzene must equal the chemical potential of toluene in a benzene-toluene mixture.

asked 2022-05-15

A new linear temperature scale, degrees Zunzol ${(}^{\circ}Z)$, is based on the freezing point and boiling point of a newly discovered compound zunzol. The freezing point of zunzol $-{117.3}^{\circ}C$, is defined as ${0}^{\circ}Z$, and the boing point of zunzol, ${78.4}^{\circ}C$ is defined as ${100}^{\circ}Z$. What is the freezing point of water in degrees Zunzol?

asked 2022-04-26

Why the E of the time component 4-momentum is the total energy and not another?

The time component of the 4-momentum is $E/c$, and I saw that it is the "total energy" and from here we can derive the formula ${E}^{2}=(pc{)}^{2}+{m}^{2}{c}^{4}$

$E$ is the total energy? Can't it be some multiple of it or just some other energy?

The time component of the 4-momentum is $E/c$, and I saw that it is the "total energy" and from here we can derive the formula ${E}^{2}=(pc{)}^{2}+{m}^{2}{c}^{4}$

$E$ is the total energy? Can't it be some multiple of it or just some other energy?

asked 2022-05-08

What conditions are necessary for the free-energy change to be used to predict the spontaneity of a reaction?

asked 2022-07-22

Scientists say that it is impossible to reach a temperature of zero kelvin, because the atoms will stop moving, and the volume of the substance will become zero, But we have reached the pico kelvin temperature, which is almost zero, and there is no difference between it and zero, so why do they say it is impossible? and The laws of physics still work at picokelvin.