Intermediate Thermodynamics Questions & Answers  




The polynomials used to generate the chart cannot be used in those regions. There are 2 reasons for this: (i) the substance has too little compressibility (it's a solid, an “incompressible” liquid) or (ii) we're too far away from the critical point and the polynomials lose some accuracy for low $T_{\rm R}$ and low $P_{\rm R}$. I'll give you 1.5 point bonus boost for this question.




Please contact me by email for such an issue. This thread is for questions related to the course material.. To answer your question, 30 minutes before class time is too late to notify me.. You have to notify me one day ahead. If you don't come to class in 20 minutes, you'll lose 4 points for attendance and 3 points for the assignment. I have many body aches too, but I come and teach just the same... ;)




A vapor is any gaseous substance at a temperature less than its critical temperature. Generally speaking, any gaseous substance such as oxygen, nitrogen, water, etc can be a vapor. However, in assignment #8 (psychrometrics), a vapor denotes only water and not oxygen or nitrogen or any other gaseous substance. This is because psychrometrics in this course is used only to solve airwater gaseous mixtures where the temperature of the mixture is less than the critical temperature of water and above the one of air — therefore, gaseous oxygen/nitrogen are not vapors but gaseous water is. I'll give you 1 point bonus boost for this question.




About Assignment #8 Question #3, there was an error in the question formulation. I changed it yesterday: please check the latest version. About the second question you have, I don't understand your notation. I guess you mean $\dot{m}$ instead of $m^\prime$? Please fix your notation and I'll answer your question.. 



I don't understand... How exactly do you find the enthalpy from Figure A9 (psychrometrics chart)? Please explain better your question, then I can answer it.




Yes in class, I mentioned that: $$ \underbrace{\sqrt{\frac{3 k_{\rm B} T_{\rm N}}{m_{\rm N}}}}_\textrm{approximate} \approx \underbrace{\sqrt{\frac{8 k_{\rm B} T_{\rm N}}{\pi m_{\rm N}}}}_\textrm{exact} $$ The approximate solution is easy to find from the definition of the temperature as outlined in the tables. The exact solution is difficult to obtain and its derivation is beyond the scope of this course. Just remember that the approximate solution is a very good approximation to the exact solution (less than 15% error). In the exam, you can use either the approximate or the exact solution. I'll give you 1 point bonus boost for this question.




At steady state, the thermodynamic properties such as $\rho$, $P$, $T$, or the gas/liquid macroscopic velocity vector $\vec{v}$ do not change in time. Therefore, all time derivatives involving the macroscopic properties and thermodynamic properties should be set to zero at steadystate. However, the microscopic properties are not necessarily constant in time. For instance, the speed of one molecule is never zero and varies in time whether the problem is steadystate or not.. I'll give you 1 point bonus boost for this question.




When the problem involves chemical reactions, you have to calculate the entropy for each species similarly to how we calculate the enthalpy. That is: $$ s=\frac{\overline{s}^0}{\cal M} + \Delta s $$ where $\overline{s}^0$ is obtained from Table A24 and $\Delta s$ is the entropy addition calculated using perfect gas relationships if the gas is not at 298 K and 1 atm. That is: $$ \Delta s= C_P \cdot \ln\left(\frac{T}{\rm 298~K}\right)  R \cdot \ln \left( \frac{P}{\rm 1~atm} \right) $$ I'll give you 1 point bonus boost for this question.




Please fix your post and typeset the mathematics correctly. Also, don't use unclear abbreviations, write the words fully. After your post is fixed I will answer your question.



$\pi$ 