Question

At high temperatures, which one of the following empirical expressions correctly describes the variation of dynamic viscosity $\mu$ of a Newtonian liquid with absolute temperature $T$? Given: A and B are positive constants.

• A. $\mu = A + BT$
• B. $\mu = A \exp\left( \frac{-B}{T} \right)$
• C. $\mu = A \exp(BT)$
• D. $\mu = A \exp\left( \frac{B}{T} \right)$

Hint:

At high temperatures, the dynamic viscosity of a Newtonian liquid often follows an exponential relation with temperature, where viscosity decreases as temperature increases. This behavior is commonly described by the equation $\mu = A \exp\left( \frac{B}{T} \right)$.

Answer 1

The Correct Option is D

In many empirical models for dynamic viscosity $\mu$ of liquids, especially Newtonian liquids, the relationship between viscosity and temperature is often given in the form of an exponential dependence. 
Step 1: Understanding the options 
- Option (A): Incorrect — This option suggests a linear relationship between viscosity and temperature, which is not typically the case for Newtonian liquids at high temperatures. 
- Option (B): Incorrect — This option represents a decrease in viscosity with increasing temperature, but this is not a typical form for high-temperature behavior of Newtonian liquids. 
- Option (C): Incorrect — This option suggests an increase in viscosity exponentially with increasing temperature, which is not typical for Newtonian liquids. 
- Option (D): Correct — This option represents the correct form, where viscosity decreases exponentially as temperature increases, a common behavior for many Newtonian liquids. This equation fits the empirical models of viscosity variation with temperature at high temperatures. 
Step 2: Conclusion Thus, the correct expression for the variation of dynamic viscosity $\mu$ with temperature $T$ is given by $\mu = A \exp\left( \frac{B}{T} \right)$. Hence, the correct answer is Option (D).