Question by Student 201227128 As doing assignment#6 question #2 there is something I want to ask about constant "$a$". In Van der Waals equation the unit of "$a$" is $[\frac {Pa \cdot m^6} {kmol^2}]$. But in Redlich-Kwong equation, I found that the unit of "$a$" is $[\frac {Pa \cdot m^6} {kmol^2 \cdot K^{1/2}}]$. Then should i derive another equation of "$a$" for Redlich-Kwong equation?(In table I could not find equation about "$a$" except at Van der Waals equation and Berthelot equation which are same.)
 05.12.14
Yes you have to derive an expression for $a$ for the Redlich-Kwong or Benedict-Webb-Rubin equations of state. It will be different from the $a$ of the Van der Waals or the Berthelot equations of state. I'll give you 1.5 bonus boost points for this question.
 05.13.14
Question by Student 201227128
As I doing the assignment#6, I find strange things at $Figure A-1$. At $Figure A-1$(Generalized compressibility chart), for $T_R=0.95$, $T_R=0.90$, $T_R=0.85$, $T_R=0.80$, $T_R=0.75$, $T_R=0.65$, $T_R=0.60$ (red parts,except $T_R=0.70$), the lines(funtions) are not continuous. Then, can we know compressibility factor at no graph parts for these $T_R$ values? (similarly $v'_R$ also is not continuous.(blue parts) ) please check the picture. 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.
 05.15.14
 Question by Student 201127146 Good afternoon Professor, I'm sorry to say I cannot present your lecture today. I have my body aches all over... even hard to keep awake. If you admit body aches for reason to be absent, what should I submit for evidence? Thank you for read this.
 05.20.14
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... ;)
 05.21.14
 Question by Student 201327150 I don't know what is vapor. Is vapor always water? or Will I assume vapor is water. I feel so confused.
 05.25.14
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 air-water 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.
 Question by Student 200927143 Hi, professor. I had a few questions on studying.\begin{alignat}{1}\end{alignat} First, a question about using the table A-2. On solving assignment 8 question #3, I got a T=14.5 Celsius to find saturated vapor. But the table A-2 has not point data. I found that temperature was not directly proportional to saturated vapor. How can I approach this problem?\begin{alignat}{1}\end{alignat} Second, according to your lecture about Evaporative cooler on 21st may. We used a lot of process to solve problem. One of them 'mass conservation for H2O' is \begin{alignat}{1} \dot{m} _{V2} & = \dot{m}_W+\frac{\omega_1 \dot{m}_1}{1+\omega_1}.\end{alignat} I was so confused whether 'mass flow of wetted' contains 'mass flow of air'. So my question is, To use 'mass conservation for H2O', Is it possible containing a 'mass flow of wetted' which is not saturated vapor. Have a nice day! ^_^\begin{alignat}{1}\end{alignat} Thank you! I understand what you said. But I can't find the latest version. Is it posted on your web site?
 05.27.14
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.. Hm, I guess you are confused about the last term in your equation. Essentially, the mass conservation of water includes only water vapor and liquid water, not air. Thus, assuming there is no liquid water coming out because all the liquid evaporates, mass conservation of water entails that: $$\underbrace{\dot{m}_{\rm V2}}_{\textrm{vapor going out}}=\underbrace{\dot{m}_{\rm W}}_{\textrm{liquid going in}}+\underbrace{\dot{m}_{\rm V1}}_{\textrm{vapor going in}}$$ Then, it can be easily shown that: $$\dot{m}_{\rm V1}=\frac{\omega_1 \dot{m}_1}{1+\omega_1}$$ Thus: $$\underbrace{\dot{m}_{\rm V2}}_{\textrm{vapor going out}}=\underbrace{\dot{m}_{\rm W}}_{\textrm{liquid going in}}+\underbrace{\frac{\omega_1 \dot{m}_1}{1+\omega_1}}_{\textrm{vapor going in}}$$ Please fix your notation again: $w$ should read $\omega$. Then I'll give you 1.5 point bonus boost for this question.
 Question by Student 200927141 Professor, This is problem about enthalpy. When I solve the problem4 on Assignment #8, I tried to use Table A-2. But i can't solve the problem. But When i use the Fig A-9, It was ok. so i just substitute Celsius temperature on formula instead of Kelvin. It's working. i thought enthalpy is function of Kelvin. But this one need to solve using Celsius... Previous question (1,2) usually need difference of temperature, so i didn't need to worry. Can i know the reason why it's working only for a celsius?
 05.28.14
I don't understand... How exactly do you find the enthalpy from Figure A-9 (psychrometrics chart)? Please explain better your question, then I can answer it.
 Question by Student 201214353 Professor, I have a question about chemical reaction rate lecture. In lecture, you say $$\bar {q_N} \approx \sqrt{\frac{3k_B T_N}{m_N}} \\ \bar {q_N} = \sqrt{\frac{8k_B T_N}{\pi m_N}}$$ Thus : $$\sqrt{\frac{3k_B T_N}{m_N}} \approx \sqrt{\frac{8k_B T_N}{\pi m_{N}}}$$ But I don't understand how are these two equations the same. And what is the meaning of $$\bar {q_N} = \sqrt{\frac{8k_B T_N}{\pi m_N}}$$
 06.02.14
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.
 Question by Student 201127116 Professor, I have question about Steady-state. I guess, All molecules doesn't move or there isn't any other change of form. Is it right? And why we could erase $$\frac{d}{dt}\int_V \rho dV$$ in Stdeay-state? You had taught about Steady-state. But i didn't make sense about Steady-state.
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 steady-state. 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 steady-state or not.. I'll give you 1 point bonus boost for this question.
 Question by Student 200927141 Hi, professor. I'm trying to solve the assignment#9. In the problem2,3,5, we used the enthalpy formula including enthalpy of formation and additional enthalpy when it's not 298K. But in problem6, how do i use entropy form? Do i just use the entropy change in a perfect gas ??
 06.03.14
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 A-24 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.
 Question by Student 201027146 In assignment 9, problem number 2 (b) In energy equation, Q dot = 0 ( you said "Q dot is heat trans only in this course, not heat due to chem proc) In assignment 9, problem number 3 (b) The question is to determine the rate of heat transfer (=Q dot) so I think this case is also Q dot = 0 (The answer is 0) is it true? there is something that I miss?? I hope to know your opinion....
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.
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 $\pi$