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The partition function $Z$ is defined as
$$Z(T,\mathbf{x})=\sum_{\{\mu\}}e^{-\beta \mathcal{H}(\mu)}$$
where sum is over microstate ($\mu$).
For an ideal gas,
$$Z(T,V,N)=\int \frac{1}{N!} \prod_{i=1}^N\frac{d^3q_id^3p_i}{h^3}\exp\left[-\beta \sum_{i=1}^N\frac{p_i^2}{2m}\right]$$
$$Z(T,V,N)=\frac{1}{N!}\left(\frac{V}{\lambda(T)^3}\right)^N$$
$$\Rightarrow \...
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The most probable speed, $v_{mp}$ is by definition the position of the maximum of the curve $f(v)$. Since this curve is asymmetric and skewed to the right, the mean is greater than the position of the maximum (they are equal for symmetric curves, but it couldn't be symmetric in our case, since $v$ is always positive, i.e., bounded from the left, but not from ...
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When a candle is lit, the smoke has some wax content that can be lit. This is why you can quickly relight the candle by putting a match against this smoke. However, the rest of the air does not have any wax content, so will not be lit by the match's flame. Also, the smoke is only lit on fire for a very short amount of time, so even if your fingers were close ...
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This is a long comment:
Here is a simple plane electromagnetic wave:
Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This 3D animation shows a plane linearly polarized wave propagating from left to right. The electric and magnetic fields in such a wave are in-phase with each other, ...
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The answers provided by other users are very good. But I put this answer as completing them (albeit small). So, the other users can see different viewpoints in this page.
In real life, some processes take place at constant pressure and also at constant temperature. Gibbs Free Energy ($G$) is simply a (Legendre) transformation of energy ($G=E+PV-TS$) in order ...
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Kinetic energy of electrons due to electric current $I$ in an inductor is much smaller than magnetic energy $\frac{1}{2}LI^2$ (provided the inductor has large enough $L$, which is usually the case).
So yes, strictly speaking total energy stored in the capacitor is transformed into magnetic energy and kinetic energy of current-carrying charges, but the latter ...
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Nuclear binding energy can be seen as a "special form" of binding energy. You can see that the given definition for the latter
the amount of energy required to separate particles from a system
also applies to a nucleus: In this case, the particles are the nucleons and the system is the nucleus.
The only difference, as you noted is that in one of ...
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My textbook says that internal energy for a system can only be defined
if the system is isolated i.e. it has no external $K.E.$ and is not
present in any external force field. But why?
It is because it is the internal energy, $U$ of the system. The internal energy is defined as the sum of the kinetic and potential energies of the atoms and molecules of the ...
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The answer really depends on the context.
In many cases the internal energy is defined as the energy of the interaction between the parts of the system. In this case it is easily separable from the kinetic energy and the energy due to the external force fields.
However, in the context of statistical physics, the internal energy usually includes the kinetic ...
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The de Broglie equations relate the wavelength $\lambda$ to the momentum $p$, and frequency $\nu$ to the total energy $E$ of a free particle:
$$\boxed{\lambda=\frac{h}{p}; \ \ \ \ E=h\nu}$$
or
$$E=\hbar \omega , \ \ \ \mathbf{p}=\hbar\mathbf{k} $$
Reference : Matter Wave
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My guess would be that originally the degree was the nightly shift in the position of the stars in the sky, but as with the original defnition of the meter, they didn't get it quite right. Or, mabe someone later decided to round it so that number of degrees in a circle could be factored.
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Apart from the temperature, the units measured in degrees are referring to something periodic (for example, the phase of oscillations), which can then be reduced to angle, and consequently measured in degrees ($1/360$ of the full circle), grads ($1/400$ of the full circle) or radians. Angles are obviously dimensionless.
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In some ways this is not a question about Physics rather one needs to look at the etymology of the word degree. Latin *degradus "a step", and so the notion of "one of a number of subdivisions of something". As to the angle measure it is a legacy of counting to base $60$, sexagesimal, by the ancient Sumerians in the 3rd millennium BC ...
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f you have a constant power output then the acceleration will not be constant. It will actually decrease as the rocket speeds up. This is because $P=Fv$ (for motion in one direction). As the velocity $v$ increases, the force $F$, and hence the acceleration, must decrease.
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As you suggest, the thought experiment can be stated in a clear way when all the components in the setup are mechanical parts.
Heavy machinery usually as a type of clutch that is called 'torque convertor'. Let's say we have a machine with a a powertrain such that if the load increases the power output increases to meet the load, so that the drive axis is ...
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This is often a point of confusion for people new to the concept of work in the physical sense. If we strictly look at the motion of the baby, carrying it is equivalent to placing it in a stroller and pushing it across the room. You can see that the stroller is not doing any work to keep the baby at the vertical position it is in. Assuming the stroller ...
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The definition of work made by a force is $$W=\int\vec{F}\cdot d\vec{r},$$ where $\vec{F}$ is the force and $d\vec{r}$ a differential displacement.
In your case, the force to hold the baby is "upwards in the vertical" (opposing to gravity), and the displacement is "horizontal", i.e. parallel to the floor, so the dot product between the ...
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Well I am going to try and make this as simple as possible.See the definition of work is :
Work is defined as the product of a Force and displacement of the point of application of force in the direction of displacement.
As you can see in the bolded section Work done on a body has no relation to the displacement of its centre of mass.It merely depends on ...
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Now let's say a ball is rolling, friction acting on it (Assuming any other necessary forces act too). Now we say that as the bottommost point is always at rest(point of contact), work done by friction is 0 (pure rolling). But why exactly do we see only the point of contact and not the centre of mass ?
The friction force acts on the contact patch, not on the ...
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What's Gibbs free energy?
$$G=H-TS \ \ \ \text{Gibbs function}$$
Suppose a system in contact with surrounding at temperature $T_0$ and pressure $p_0$. If heat $\delta Q$ enters the system,
$$\delta Q=dU-\delta W -(-p_0dV)$$
where mechanical work added to the system from the work $-p_0dV$ done by the surrounding due to the volume change of the system.
$$T_0dS\...
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Gibbs free energy is a thermodynamic potential which is derived using Legendre trasformation of $U(S,V,N)$ (fundamental relation) for a thermodynamic hydrostatic system.
$U(S,V,N)\to G(T,P,N)$ using Legendre transformation
$G(T,P,N)=U-TS+PV$
$dG=dU-TdS-SdT+PdV+VdP \tag{1}$
By first law of thermodynamics,
$dU=dQ-PdV+\mu dN$
Substitute $dU$ in (1),
$dG=(dQ-PdV+...
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