From 3a537f75450972590d8084ce8a2f80d3a7046998 Mon Sep 17 00:00:00 2001 From: Nathan Nguyen <159226326+Indigo5684@users.noreply.github.com> Date: Wed, 15 Jan 2025 11:54:09 -0600 Subject: [PATCH] Thermal Physics Reading Assignment 2 --- docs/physics/thermal/1-energy.md | 42 ++++++++++++++++++ .../Reading Assignment 2.rnote | Bin 0 -> 716571 bytes 2 files changed, 42 insertions(+) create mode 100644 statics/physics/thermal/reading-assignments/Reading Assignment 2.rnote diff --git a/docs/physics/thermal/1-energy.md b/docs/physics/thermal/1-energy.md index 0cde831..cf9d02f 100644 --- a/docs/physics/thermal/1-energy.md +++ b/docs/physics/thermal/1-energy.md @@ -97,3 +97,45 @@ In monoatomic molecules, each molecule has $3$ degrees of freedom, corresponding Additionally, there exist modes of vibration, which each contribute two degrees of freedom (positional energy and vibrational kinetic energy). At room temperature, these are negligible in gasses. In solids, each atom may vibrate in three directions (as there are 3 translational axis), but atoms may not rotate, leading to $6$ total degrees of freedom. In liquids, we are sad. + +## Section 1.4 - Heat and Work + +We are familiar with energy, temperature, and work. + +**Theorem**. The Law of Conservation of Energy. Energy cannot be created or destroyed, only moved. + +**Theorem**. In thermodynamics, energy may only enter or leave a closed systeem via *heat* and *work*. + +**Definition**. *Heat* is any spontaneous flow of energy between two objects due to a difference in temperature. + +**Definition**. *Work* is any other flow of energy in or out of a system. + +With $U$ being the total energy of a system, we can write + +$$\Delta U = Q + W$$ + +That is, the change in total energy of a system is equal to the heat being added to the system and work done on the system. + +Note that with heat engines, we often see $Q - W$, where $W$ instead represents the work done by the system. + +**Theorem**. The First Law of Thermodynamics. $\Delta U = Q + W$, along with the Law of Conservation of Energy. In other words, you can't win the game. + +**Definition**. The SI unit of energy is the *Joule*, where $1J = 1 \text{kg} \vdot \text{m}^2 / \text{s}^2$. + +**Defitition**. The imperial unit of energy is the *calorie*, or the amount of energy to heat one gram of water by $1 \degree \text{C}$. The exact conversion factor is defined as $1 \text{J} = 4.184 \text{cal}$ + +**Definition**. *Conduction* is the transfer of heat by molecular contact, in which fast moving molecules bump into slow moving molecules and transfer energy. + +**Definition**. *Convection* is the transfer of heat by the bulk motion of a liquid or gas. + +**Definition**. *Radiation* is the transfer of heat via electromagnetic waves. + +## Section 1.5 - Compression Work + +From classical mechanics, we know that $W = \vec{F} \cdot d\vec{r}$. + +Consider a piston with a compressable gas. In tthis case, with $\Delta x$ positive as the piston moves inwards, we can state that $W = F \Delta x$. Now, we want the gas to always maintain internal equilibrium. For this to be true, the piston must be moving relatively slowly. Note that any volume change that happens in this way is said to be *quasistatic*. + +We know that the force exerted by the piston is equal to the pressure times the area. Thus, $W = P A \Delta x$. But $A\Delta x$ is just volume (in this case, negative, as volume is decreasing). So, $W = -P \Delta V$. + +However, this assumes constant pressure. For a non-constant perssure, $P(V)$, we know that $W = \int F dx = - \int P(V) dV$. \ No newline at end of file diff --git a/statics/physics/thermal/reading-assignments/Reading Assignment 2.rnote b/statics/physics/thermal/reading-assignments/Reading Assignment 2.rnote new file mode 100644 index 0000000000000000000000000000000000000000..d7a8f654dbc030803edaa26c17becd2198f493dd GIT binary patch literal 716571 zcmd42`8!nqAOBwom1-jHN=xOh{gY2^At^O-cz_hA~qpyCJe}^ zzLV@KQ?|ii%#0ak|9XEvpMT+dUEgz^pU!ozbDrm%=ea*0kNe~H045yR^Z#ywwH6<{ zQ&wNAd2sHXh^u=~7q7-{3yBDc_$IVks#rhQj6;ZMtxXAd_k)NlWj`Gq({8)hOiI^c z|2Wv)S^ToZfMVG(^&u+unOHvEXN@@TA;{m^!oftFwwrd3K(R+b7;6oHAUvcoJR$@c z1Qd+6j`Q0)|DEM;kCq9z*oyLTZix3IE*zV`h?@viMq6DGFjlAwfB8G3=&qc!w2x?v zZW*7kva`9c>;Tc#x-t>ZHyqESzJZnh<6`Kn&;gz2 z&xRsjnlS~GX@OuEbe}Ry1kQHZM?4EcZ?9m{JCr}Y{r`3!mbet%Y{(xL+;pLBbj{vO zX9u&`^gpBzqKF4rYmIP~OqJ~zni%yvZ=1ckp^S142ygjAZ`wJ|3;`YW(`vJCnf+6M zTov%Ky|oo+Sn$31kL8!gWr3OhvQIp=;u}1wS2=gCtMK6?rAPg5rxWBUJ&!#E@%Pl7 zDgEQ)rpU8{akahFyC0?>SzpPq%iCei5?%7-`;wfU;rIJ`dhc+F0@fJO5S@Z+MCw5W z_S$t`!|8if<`?&&w<_xV&lB!v3?)q4d zAVQtBJ=D=!;zn1^(!NpR?aJ5Z1FnFyh3Z=mYTTlk801QphMi zJ8W5316LM?bg^i;bbWcl4%$fkC8ukreUQUEW_zq;|B>nE+ljse%!4^@SiSdBKC?ct zu-Q%%>RpP#zw0i->HJCN4twdSXPL1uyk7_&d0?v|73%$aauJ9bSinr5F^OQbe5NhZ zahx>401cJXofgx+Jn8WPe)kWhecQ}KR1A2JA9l+9Ji$=#e6lFQKic{0NyA5P(vmhR ze5$Z@-_p@L&=32}n<>~ToPJwdoh?9qS;u3y1?PO@_PKQgeDb{KZhDt9 z{bA492&DhIH{pz3SvODfjd{^9&{E#T<&@2su9depit%Q+td2={#=@?+A2^{q@^fbT zW1};2Ru_20Q7S^JR}pk-+FGUoda~BHISX^sgXB*7S=D#mb(@0?#EPbeoJ+<9H|3E_ zE;lKhyE_~Vp@qeMBYT{inK?mmgjsWuC*2#lJ@Y(>ME~E9vQjULNy{MIIw z8kF>4a11l5R-_7y{z#uFK(O@rE#5=-pc8{%4{R>k@PFyHJn%fW$kRbJx2(*-yP!C( zB}K65eQn$?eu+pKu!aV+_+_}qaQ2Pkt(^Kv@T~f91Do-$jan>wdfTAdSV^ z=;*pE6f$bOuMCA;8KjR7+Cr~R%{+XU@6efe;#07tcL;xHBG${h{mb>o>p2*a>y!=! 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