Solving for Tpeak in Heat Capacity Question | Homework Help

In summary, the conversation involves a student seeking help with a problem involving finding Tpeak. They have successfully completed the first part of the problem and attempted the second part by setting the derivative of C with respect to T equal to 0. However, there appears to be a small mistake in their calculation and the correct equation should be (2 + theta)(Te^(theta/T) + T) = 2theta e^(theta/T) - theta^2 e^(theta/T). The expert offers to help the student and suggests trying to solve for T again using the corrected equation.
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Homework Statement



please see attached! :)


Homework Equations





The Attempt at a Solution



Ok so I've done the first part and the first bit of the second, so I've shown that theta = 2 uBB/kb

My problem is in the next bit where it asks you to work out Tpeak. I guess you have to differentiate C wrt T and set it equal to 0. I've tried this loads of times and keep getting (2 + theta)(Te^(theta/T) + T) = 2theta e^(theta/T)

which I can't solve for T!

any help would be great!
thanks :)
 

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  • #2



Hello!

I would be happy to assist you with your problem. It seems like you are on the right track by setting the derivative of C with respect to T equal to 0. However, I believe there may be a small mistake in your calculation. The correct equation should be (2 + theta)(Te^(theta/T) + T) = 2theta e^(theta/T) - theta^2 e^(theta/T). Can you try solving for T again using this equation? Let me know if you are still having trouble and we can work through it together. Good luck!
 

1. What is heat capacity?

Heat capacity, also known as specific heat, is the amount of heat energy required to raise the temperature of a substance by a certain amount. It is a physical property that is specific to each substance and is typically measured in units of joules per degree Celsius (J/°C) or calories per gram per degree Celsius (cal/g/°C).

2. How is heat capacity different from specific heat?

The terms heat capacity and specific heat are often used interchangeably, but technically, they are not the same. Heat capacity is the amount of heat energy required to raise the temperature of a substance by a certain amount, while specific heat is the heat capacity per unit mass of a substance. In other words, specific heat takes into account the mass of the substance, while heat capacity does not.

3. How is heat capacity measured?

Heat capacity can be measured using various techniques, such as differential scanning calorimetry, bomb calorimetry, or specific heat capacity measurements. These methods involve applying a known amount of heat to a substance and measuring the resulting change in temperature.

4. What factors affect heat capacity?

The heat capacity of a substance is affected by its mass, composition, and physical state. Generally, substances with higher mass and/or more complex molecular structures have higher heat capacities. The physical state of a substance also plays a role, as gases tend to have higher heat capacities than liquids or solids.

5. Why is heat capacity important?

Heat capacity is an important concept in thermodynamics and plays a crucial role in understanding and predicting the behavior of substances in various processes, such as heating and cooling. It also helps in designing and optimizing systems that involve heat transfer, such as engines and refrigeration systems.

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