Van Der Waals Constants k b = 1.38 x J K -1 Substance. Substance

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Coral Banks
5 years ago
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1 Cheistry 45 Physial Cheistry I Exa I Given Info: R 8.35 J ol - K - Van Der Waals Constants k b.38 x 0-3 J K - Substane a b P T (J. 3 /ole ) ( 3 /ole) (MPa) (K) Air x K Carbon Dioxide (CO ) x K Nitrogen (N ) x K Hydrogen (H ) x K Water (H O) x K Aonia (NH 3 ) x K Heliu (He) x K Freon (CCl F ) x K A 0 a B 0 b Pa 6 ol ol ol ol ol - He Ne Ar H N O Air CO CH Substane

2 . No one an ever say I didn t ake you plug and hug a. For 0.53 oles of CO in a.5l vessel at 300K, assuing the Beattie- Bridgan value for the pressure is the true value, what is the perent error given by the Ideal Gas equation and by Van Der Waals? V.5/ L/ol /ol Beattie-Bridgean A (-7.3 x 0-6 /0.0083) B x 0-6 (-7.35 x 0-6 /0.0083).008 x P ( x0 ) N Ideal P RT/V 8.35*300/ N - Van Der Waals N 5 P x % error Ideal ( 00) 4.49% % error VDW ( ) 0.70% b. What is u for O at 300K? u 3RT x0 s M If I said that Fred and Wila, on average, were oving at.3 /s and 6.77 /s respetively at the sae teperature, then what is the ratio of their asses? u M so we an say that u u W F M 6.77 F. Fro here, 6. 3 M W.3

3 d. Ok, so let s say, for the sake of arguent, that He is an ideal gas. I deide to put a ole of it in an expandable vessel and do a ouple things. First, I inrease the pressure real fast like fro 4 Pa to 63 Pa at 73 K. What is the agnitude of the work here? Is work being done on the gas or is it doing work on e? Now, being real exited about that result, I deide to sit for infinity and perfor the experient again over that period of tie. What is the agnitude of the work now? What perentage of the energy I observed the seond tie was not seen the first tie? V nrt/p (8.35)(73)/4 6 3 and siilarly, V 36 3 w irr -P (V V ) -4(36 6) 764 J/ol work done on syste w rev V V PdV nrt V V dv V V nrt ln V ln J ol Finally, the perent not seen the first tie is ( )/344*00 48%

4 . Now to business. Modeling! I put a bunh of ants on the floor of a very thin tank. The tank is sloped downhill as shown. I then put soe haburger at the top of the slope. This generates a tendeny for the ants to ove towards the food, but this tendeny is biased by gravity. Now soe ants are hungrier than others and have ore drive to reah the food. Soe are repulsed by the food (vegetarians), and soe are indifferent to it. This eans that the ants are not experiening this situation equally, in fat, one ould desribe the fore that drives their position at a given tie along the line ab as a distribution. Ok, so let s define their drive to reah the food as z and the ants are experiening a distribution, φ, of drive at a snapshot in tie as the following: g a eat 60 o 30 o z b φ ( z ) σ e π ( z z0 ) ( )dz σ This happy equation ay be failiar to soe of you. It is the forula for a bell urve with z o being the average value of z and σ being the standard deviation. Ok, so a given ant has z for its drive. Now the fore experiened by eah ant is siple: F ant z - F g These are diretional fores, but we are only onerned with the diretion along the floor of the tank so they an be treated as salars using only sign to designate diretion. With this in ind, let s start the proble a. What is the fore experiened by eah ant due to gravity along the floor of the box. (Hint: this should be parallel to and in the opposite diretion of the arrow z above) g 60 o F g The diagra to the right desribes the situation. F g is the projetion of gravity along the botto of the tank. F g g osθ ½ g b. The ass of an ant is. What is the total fore experiened by eah ant along the floor of the tank? F ant z - ½ g

5 . In ters of variables only, what fration of ants are oving towards the food? (Only set this one up, I want to see all the relevant paraeters) The ant is oving towards the food for all values of z that are greater than the fore fro gravity. Matheatially, this is when z > ½ g. the distribution of the values of z is represented by φ(z) so the final expression is f g z> g φ ( z) ( z z ) 0 σ σ π g e dz 3. a. If the ratio of P /P / and the ratio of V /V /3, then what is T if T 98 K? ( PV ) T ( P V ) T 3 T 98 T 788 K b. For substane above, the virial oeffiients are desribed as the following: b i 3 X T i T T where b - i- ( ) i i For V, at what values for T does the gas behave ideally? (use the seond, third and fourth virial oeffiients) For V, Z + B(T) + C(T) + D(T) + ½ T - T + 3 T 3 + ¼ T T 4 so the gas will behave ideally for all roots of ½ T - T + 3 T 3 + ¼ T T 4 0 this has two roots at T 0 and two ore roots defined by ½ T T + ¼ T T 0 we an find quadrati roots by the quadrati forula: T 3 ± 9 4 T 4 T 3T ± , 536 T All this to say that these roots are not physial reality, so the only plae where this gas would behave ideally is at T 0.

6 4. Given this relationship: (not a real relationship, treat it as ideal) U ( T ) V lnt Using only relationships derived last week, give expressions for the following in ters of R and P: C V, C du dt V V, V, T R P C P, (do not use C p, C v, + R) C dh and H U + RT V lnt + RT RT/P ln T + RT P, dt P, so C dh R R lnt + dt P P P, + P, R Finally, derive a relationship between C P, and C V,. Should this gas be treated as ideal? If C V, R/P then CP, CV, ln T + CV, + R whih is different fro the ideal relationship, C P, C V, + R, so it should not be treated as ideal.

Problem Set 2. Chapter 1 Numerical:

Problem Set 2. Chapter 1 Numerical: Chapter 1 Nuerical: roble Set 16. The atoic radius of xenon is 18 p. Is that consistent with its b paraeter of 5.15 1 - L/ol? Hint: what is the volue of a ole of xenon atos and how does that copare to