Q4.1 According to Debye's formula in physical chemistry, the orientation polarization P of a gas satisfies 4 P-N() 3 3kT where u, k, N are positive constants, and I is the temperature of the gas. Find the rate of change of P with respect to T.
Q4.1 According to Debye's formula in physical chemistry, the orientation polarization P of a gas satisfies 4 P-N() 3 3kT where u, k, N are positive constants, and I is the temperature of the gas. Find the rate of change of P with respect to T.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please only answer 4.1
![### Question 4:
**Use a linearization of \( g \) to approximate \( g(1.01) \). Round to 2 decimal places.**
#### **Q4.1**
According to Debye's formula in physical chemistry, the orientation polarization \( P \) of a gas satisfies
\[
P = \frac{4}{3} \pi N \left( \frac{\mu^2}{3kT} \right)
\]
where \( \mu, k, N \) are positive constants, and \( T \) is the temperature of the gas. Find the rate of change of \( P \) with respect to \( T \).
#### **Q4.2**
The frequency of standing waves on a violin string of length \( L \) and linear density \( \rho \), which is stretched to a tension \( T \), is given by
\[
f = \frac{1}{2L} \sqrt{\frac{T}{\rho}}
\]
Then the rate of change of the frequency with respect to a tension \( T \) is given by \( \frac{df}{dT} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2cc04b1e-803c-4d9d-b550-d2ae04bcc2b3%2F6c8499c7-acc6-466b-a02b-2c58a000e155%2Fcha2ft5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 4:
**Use a linearization of \( g \) to approximate \( g(1.01) \). Round to 2 decimal places.**
#### **Q4.1**
According to Debye's formula in physical chemistry, the orientation polarization \( P \) of a gas satisfies
\[
P = \frac{4}{3} \pi N \left( \frac{\mu^2}{3kT} \right)
\]
where \( \mu, k, N \) are positive constants, and \( T \) is the temperature of the gas. Find the rate of change of \( P \) with respect to \( T \).
#### **Q4.2**
The frequency of standing waves on a violin string of length \( L \) and linear density \( \rho \), which is stretched to a tension \( T \), is given by
\[
f = \frac{1}{2L} \sqrt{\frac{T}{\rho}}
\]
Then the rate of change of the frequency with respect to a tension \( T \) is given by \( \frac{df}{dT} \).
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