The vibrational contribution to the heat capacity is given by e-eV /2T Cm = R -e-eV/T Show that in the high temperature limit (when 0' « T) T. = R. (HINT: for small values of x, e* = 1+ x). Explain each step in your derivation.
The vibrational contribution to the heat capacity is given by e-eV /2T Cm = R -e-eV/T Show that in the high temperature limit (when 0' « T) T. = R. (HINT: for small values of x, e* = 1+ x). Explain each step in your derivation.
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the vibrational contribution to the heat capacity is given by the photo below. show that in the high temperature limit C=R.(For small values of x, e^x=1+x)
![The image contains a physics problem regarding the vibrational contribution to heat capacity. The problem is as follows:
**The vibrational contribution to the heat capacity is given by:**
\[ C_{V_m} = R \left( \frac{\theta_v}{T} \right)^2 \frac{e^{\theta_v/T}}{(e^{\theta_v/T} - 1)^2} \]
**Show that in the high temperature limit (when \(\theta_v \ll T\)):**
\[ C_{V_m} = R \]
**(HINT: For small values of \(x\), \(e^x = 1 + x\). Explain each step in your derivation.)**
Below this, there is a partial derivation that uses the hint provided:
\[ e^{x} \approx 1 + x \]
\[ C_{V_m} = R \left( \frac{\theta_v}{T} \right)^2 \]
The task is to derive the expression for \( C_{V_m} \) in the high temperature limit, using the approximation for small \(x\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9761b52-c7ac-4418-be0a-fc5dc6cb9c42%2Faddc7091-faae-441d-976f-c74a2184ffab%2Fj5voni_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a physics problem regarding the vibrational contribution to heat capacity. The problem is as follows:
**The vibrational contribution to the heat capacity is given by:**
\[ C_{V_m} = R \left( \frac{\theta_v}{T} \right)^2 \frac{e^{\theta_v/T}}{(e^{\theta_v/T} - 1)^2} \]
**Show that in the high temperature limit (when \(\theta_v \ll T\)):**
\[ C_{V_m} = R \]
**(HINT: For small values of \(x\), \(e^x = 1 + x\). Explain each step in your derivation.)**
Below this, there is a partial derivation that uses the hint provided:
\[ e^{x} \approx 1 + x \]
\[ C_{V_m} = R \left( \frac{\theta_v}{T} \right)^2 \]
The task is to derive the expression for \( C_{V_m} \) in the high temperature limit, using the approximation for small \(x\).
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