Intermediate Thermodynamics Questions & Answers  
Question by Student 201027111
( find heat needed to go from b2 to b3) prof said 1st law thermo can't use because unknown veriable is two with pdv and Q but in process V is constant so $dv = 0$ then $d(me) = Q$ then intergral and we can get $me_{b3} - me_{b2} = Q$ and assume calorically perfect gas $e = C_v T$ so $Q = m C_v ( T_{b3} - T_{b2} )$ we can get solve this way is wrong?
03.19.14
Please check your notation again: $dv$ is not the same as $dV$, b2 is not the same as B2, $p$ is not the same as $P$, $C_v$ is not the same as $C_V$, $me_{\rm b2}$ is not the same as $(me)_{\rm B2}$, etc. Edit your post and use the same notation as used in class, and I will answer your question.
Question by Student 201312171
Professor, I'd made a lot effort to find the way to reach equation,$\overline {q_x} = \frac {1}{4} \overline {q}$, but couldn't make simple way by integrating vectors on spherical coordinate. However, I found some other method that is to use mathmatical expression on molecules' velocity. M is molar mass, $\bar{R}$ is universal gas constant, T is temperature of gas. In <Maxwell-Boltzmann distribution>, there is proportional relation $f(q)$ that some particles have velocity $q$ among total particles, a kind of probability function about $q$. Its unit is 'per speed($\frac {1} {\frac {m}{s}}$)' $$ f(q) = \sqrt{\left(\frac{M}{2 \pi \bar{R}T}\right)^3}\, 4\pi q^2 e^{- \frac{Mq^2}{2\bar{R} T}} $$ To calcultate average value of $ q $, we should multiply it by $q$ and then integrate it in interval $(0,\infty)$. (because $f(q)$ is just a probability function about $q$) $$ \int_{0}^{\infty} qf(q)\,{\rm d}q = \int_{0}^{\infty} \sqrt{\left(\frac{M}{2 \pi \bar{R}T}\right)^3}\, 4\pi q^3 e^{- \frac{Mq^2}{2\bar{R}T}}\,{\rm d}q = \sqrt[2]{\frac{8\bar{R}T}{\pi M}} $$ And there is a proportional relation for having 1-D velocity on 'Maxwell-Bolztmann distribution'. If some particle are moving along x-axis direction on xyz coordinate, then the relation is $$ f(q_x) = \sqrt{\frac{M}{2 \pi \bar{R}T}} \exp \left[ \frac{-Mq_x^2}{2\bar{R}T} \right] $$ Its unit is also 'per speed($\frac {1} {\frac {m}{s}}$).' To calculate average value of $q_x$, we should multiply it by $q_x$ and then integrate it in interval $(0,\infty)$. $$ \int_{0}^{\infty} q_x f(q_x)\,{\rm d}q_x = \int_{0}^{\infty} q_x \sqrt{\frac{M}{2 \pi \bar{R} T}} \exp \left[ \frac{-Mq_x^2}{2\bar{R}T} \right]\,{\rm d}q_x = \sqrt[2]{\frac{\bar{R} T}{2\pi M}} $$ Therefore, comparing two average values of $q$ and $q_x$, there is the relation we've been to figure out. $$ \bar{q_x} = \frac{1}{4} \bar{q} $$ I think I should be more hard to make progress on calculating on spherical coordinate. Thanks for reading. Addition : I'm so sorry that I made many mistakes on it. I modified the things. Addition2 : I'm so sorry, sir... I don't know why its unit is wrong with that form... I get the unit that I mentioned, 'per speed'... Did I miss something...?? Addition3 : I'm really really ashamed because I confused 'molar mass' with 'molecular mass'. I really apologize sincerely...=( Reference : wikipedia(Maxwell-Boltzmann distribution, http://en.wikipedia.org/wiki/Maxwell-Bo ... stribution)
03.21.14
I don't get units of s/m for $f(q)$ as you mention. As long as the units are not consistent, I cannot give you any point for your explanation.. Please double check and edit your post. Only after the units work out will you get a bonus boost. Also get rid of the remaining line breaks. Line breaks should not be used here (they should only be used to separate paragraphs, and there's no need to have more than 1 paragraph per question/comment).
03.22.14
Question by Student 201127134
Professor, according to your lecture, there are four types of particles which can carry energy : Molecule, Atom, Electron, Photon. However, Photon, I cannot understand Photon can carry energy. I think "Photon" is just light with no mass. I think, to carry energy, particle must have mass to carry energy, but i think Photon has no mass. How can Photon can carry energy? Ofcourse, you mentioned that there are controversies wheter photon can carry energy. Would you explain how Photon can carry energy?
04.08.14
This is beyond the scope of this course, and I am not specialized in that field of engineering/physics. But I can give a quick answer. Despite being massless, particules such as photons that travel at the speed of light do carry energy following $E=h c \lambda^{-1}$ with $h$ the Planck constant, $c$ the speed of light, and $\lambda$ the frequency. I can give you 1.0 bonus boost for this question.
Question by Student 201127146
Professor, I want to ask a question abot perfect gas. To derive specific heat ratio we assumed callorlly and thly perfect gas. I wonder specific heat ratio can be used for non isobaric or non isochoric processes. Similarly, can I assume thermally perfect gas for heating process?
04.12.14
Yes we can assume thermally perfect gas or calorically perfect gas for any type of thermodynamic process. I'll give you 0.5 point bonus boost for this question. I would have given 1 point if you would have been more careful in typing your question: there are 3 obvious spelling errors ;)
Question by Student 201127146
I appreciate for your quick response. But I got another questions for assignment. In Q.4. I need to determine specific heat of water. I did my best, but it was out of my range. Can you gibe me a hint to get the value? Next, due to the lecture, entropy is associated with several bodies in one system. No mention about entropy for a body. I wonder if entropy change in 'a body' can have value under 0 Thank you for reading.
04.13.14
You can find the specific heat of liquid water or gaseous water in the tables — look through them carefully.. And yes, entropy can have a value less than zero for a body that is not isolated from its environment, this was mentioned in the last lecture.. I can not give you any bonus boost for these questions since the answers were given in class already or could be found easily.
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