Calc E as Fn of T for Ideal Paramagnet

In summary, the entropy of an ideal paramagnet is given by S=S_{0}+CE^{2}, where E is the energy and C is a positive constant. To determine the equation for E, we can use the equation 1/T = delta S / delta U and solve for E, which results in E = 1/(-2CT). This equation can be graphed as y = -1/x, dilated by 1/2C. In a paramagnet, entropy decreases as energy increases, meaning the system will willingly give away energy and increase in temperature.
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Homework Statement



The entropy of an ideal paramagnet is given by S=S_{0}+CE^{2}, where E is the energy (which can be positive or negative) and C is a positive constant. Determine the equation for E as a function of T and sketch your result.

Homework Equations



[tex]
\frac{1}{T}=\frac{\delta S}{\delta U}
[\tex]

The Attempt at a Solution



I'm fairly certain I solved correctly, but the solution seems to simple. I confused about whether the E here is the same as the U in the partial derivative equation above, in which case:

[tex]
\frac{1}{T}=\frac{\delta S}{\delta U}
\frac{\delta S}{\delta U}=-2CE
\frac{1}{T}=-2CE
E=\frac{1}{-2CT}
[\tex]

In this case, the graph appears shaped like [tex] y=-\frac{1}{x} [\tex] dilated by [tex] \frac{1}{2C} [\tex].

I reasoned that in a paramagnet entropy will decrease as energy increases, so the system will more willingly give away energy, hence increasing the temperature.
 
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Can someone tell me what I'm doing wrong with LaTex? I'm new to it and don't understand the problem with my code.
 

Related to Calc E as Fn of T for Ideal Paramagnet

1. What is "Calc E as Fn of T for Ideal Paramagnet"?

"Calc E as Fn of T for Ideal Paramagnet" is a mathematical formula used in physics to calculate the energy of an ideal paramagnetic material at a given temperature. It takes into account the temperature (T) and the number of magnetic moments (n) in the material.

2. How is "Calc E as Fn of T for Ideal Paramagnet" calculated?

"Calc E as Fn of T for Ideal Paramagnet" is calculated using the formula E = -nμBmB/(2kT), where E is the energy, n is the number of magnetic moments, μB is the Bohr magneton, mB is the magnetic moment, k is the Boltzmann constant, and T is the temperature.

3. What is an ideal paramagnet?

An ideal paramagnet is a material that exhibits paramagnetism, which is the tendency to become magnetized in the presence of an external magnetic field. In an ideal paramagnet, all the magnetic moments are perfectly aligned in the direction of the external magnetic field.

4. What is the significance of "Calc E as Fn of T for Ideal Paramagnet" in physics?

"Calc E as Fn of T for Ideal Paramagnet" is significant in physics as it helps us understand the behavior of ideal paramagnetic materials at different temperatures. It also allows us to calculate the magnetic susceptibility, which is a measure of how easily a material can be magnetized.

5. Are there any limitations to using "Calc E as Fn of T for Ideal Paramagnet"?

Yes, there are limitations to using "Calc E as Fn of T for Ideal Paramagnet." This formula is only applicable to ideal paramagnetic materials, which do not exist in real life. In real materials, the magnetic moments are not perfectly aligned and can interact with each other, leading to deviations from the ideal behavior predicted by this formula.

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