Total Energy and Voltage Change for an Electron

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Homework Statement

Alright so, there are two different parts that I am having trouble with for this question.

The first problem I need to calculate the total energy of a group of 12 electrons that each individually have a potential of 3 V. This is all that is given for the first part.

For the second part, I need to find the voltage change that occurs for an electron if the temperature gets increased by 175K.

Homework Equations

For the first part, I believe the correct equation to use would be:

E = qV

For the second part, the equation that I think would be correct is:

V = kT/q

The Attempt at a Solution

First part:

Since there are 12 electrons, I simply thought that adding up the 12 individual electrons would give the total energy for the group with the given potential. Therefore, I did:

E = 12*q*V = 12(1.602 x 10^-19 C)(3 V) = 5.767 * 10^-18 Joules

Second part:

Using the equation given and the voltage given from part 1, I thought the correct approach was to use this equation:

V_change = (k(T + 175))/q - kT/q = 175k/q = ((175 K)(1.38 x 10^-23 J/K))/(1.602 x 10^-19 C) = .015 Volts



The main things that I am worried about are the sign in part 1, the equations used for part 1 and part 2 since I'm not sure they're the correct ones, and also for the first part I'm not sure if simply multiplying by 12 since there are 12 electrons correctly gives the total energy for all of the electrons. I guess I'm mainly looking for confirmation that the equations I used were correct and that simply multiplying qV by 12 to get the total energy for a group of 12 electrons is allowed.

Thank you for any help or confirmation you can give me.

 

[KataKoniK]

Hello, thank you for your question. I am happy to assist you with finding the solutions to these problems. First, let's take a look at the equations you used.

For the first part, you are correct in using the equation E = qV. This equation represents the relationship between energy (E), charge (q), and voltage (V). Since you are given the potential (voltage) of 3 V for each electron, you can simply multiply it by the number of electrons (12) to get the total energy for the group. So your solution of 5.767 * 10^-18 Joules is correct.

For the second part, you are also on the right track with using the equation V = kT/q. This equation represents the relationship between voltage (V), temperature (T), and charge (q). However, the equation you used to calculate the voltage change is not entirely correct. The correct equation is V_change = k(T + 175)/q - kT/q. This is because the voltage change is the difference between the voltage at the new temperature (T + 175) and the voltage at the original temperature (T). So your final solution for the voltage change is correct at 0.015 Volts.

I hope this helps to clarify your doubts and confirms that your approach was correct. Keep up the good work! Let me know if you have any further questions.

 

[Mene]

Hello,

Thank you for sharing your work and concerns about this problem. It seems that you have the right idea and approach for both parts of the problem.

For the first part, using the equation E = qV is correct. And since the potential is given for each individual electron, multiplying by 12 to get the total energy for the group of 12 electrons is also correct. This is because the total energy is the sum of the energies of all the individual electrons.

For the second part, using the equation V = kT/q is also correct. However, I would suggest using the Boltzmann constant (k) in units of eV/K instead of J/K, as the charge of an electron (q) is in units of e. This would give a voltage change of 0.012 eV, which is equivalent to 0.012 V. So your final answer of 0.015 V is very close.

Overall, your approach and equations used are correct. Just make sure to pay attention to the units and use the correct values for the constants. Keep up the good work!