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1OptsQuestion 4(A monatomic ideal gas that is at some initial pressure and volume expands until its volume is doubled. During which of the following processes does ...

Question

1OptsQuestion 4(A monatomic ideal gas that is at some initial pressure and volume expands until its volume is doubled. During which of the following processes does the internal energy of the gas decrease?Adiabatic processIsothcrmal processIsobaric processThe chanpc In Internal encrgy is thc samr for all thcsc Droccsscs;

1Opts Question 4 ( A monatomic ideal gas that is at some initial pressure and volume expands until its volume is doubled. During which of the following processes does the internal energy of the gas decrease? Adiabatic process Isothcrmal process Isobaric process The chanpc In Internal encrgy is thc samr for all thcsc Droccsscs;



Answers

A monatomic ideal gas expands isothermally from $\left\{p_{1}, V_{1}, T_{1}\right\}$ to $\left\{p_{2}, V_{2}, T_{1}\right\} .$ Then it undergoes an isochoric process, which takes it from $\left\{p_{2}, V_{2}, T_{1}\right\}$ to $\left\{p_{1}, V_{2}, T_{2}\right\}$ Finally the gas undergoes an isobaric compression, which takes it back to $\left\{p_{1}, V_{1}, T_{1}\right\}$ a) Use the First Law of Thermodynamics to find $Q$ for each of these processes. b) Write an expression for total $Q$ in terms of $p_{1}, p_{2}, V_{1},$ and $V_{2}$.

During the excursion I was aspect the volume of the mono atomic ideal gas doubles in an idiomatic expansion. So by what factor do the pressure and the temperature of the guests change? So we have to find out the factor the volume devils here. Volume double in a diabetic. Sorry in A. D. A basic expansion. So for pressure we can just Right You want interview one to the power this is card comma. Which is the ratio of CP by CV. For mono atomic guests. It is their issue is 553 which is 3.66. No sorry it is 1.66. So equals two p 2. And the video to the bar. Thank Allah. So pressure to be pressure one into Be one by video calls to two comma. So pressure on and do Video equals 2-3 1. So it would be just like this. The factor for pressure we get is .5 To the power 1 1 point 6 6. So that Factor we get here is their .31 stakes into pito. So the factor is sorry it's P one. So the factories Peter by the one which is your .316. And for for the temperature we have to again and find out the factor for temperature we can right T. One interviewing comma two. We went to the program on -1 and two T. to be to come onto the -1. So in this case Teacher by T one Equals to be one divided by 3 2 into camera to the program A -1. So the factor becomes, So the factor is zero 0.5 to the power 3.66. So the factors finally results in .5 to the power .66. So the factor is 0.63- eight. After that, I was asked that to verify my answer to Part N. B. We have to consider 1 35 months of gas with an initial pressure of 333 kg basket. So initial pressure, the one 8 33 kilo pass skill An initial Volume V one which is 1.2 m Cube. You want 1.2 major cube and I have to find out the pressure and temperature of the guests after it expands A dramatically to a volume of 2.4 m too. The video equals to find four metre q. So by using these these factors, I have find out the final pressure and temperature. The final temperature would be here. The volume pulse again doubles. So the final temperature would be Now let's find out the final volume. So the final pressure 1st. So the final pressure PT would be P one into The factory. Get here is 0.316. So pressure on is going to 333 kg paschal into 0.316. So the final pressure is 1 104.28 kg has skill. So the final value uh from here we should find out the final temperature which is T one equals to pay one V 1 by N R. The mall number into the gas constant. So Initial temperature to one equals 2 Pressure one, which is 330 Kilo Paschal Interview on which is 1.2. The number of moles are given here is 135 months into the gas constant. The tomb, unequal stool, 3 52 Bryant Erdogan Caliban. So to find the final temperature, we are going to use the factor here 0.63- eight. 352.81 kelvin into 0.63- eight. The final temperature would be 223.26 Calvin. So these are the answers to get verified. My answers. Thank you.

Here we have a situation in which the more Noah told me case undergoes, um undergoes a reaction in which the William he's twice and it's a pressure is also twice here. We have more years be a pressure. So initially it was a p nod, and finally, it comes here to pee nod Mission Only when we have in ardent than final be to me. Not so. The total well done will be simply Eddie under this craft, which will be this idea that we call this a d a one in this a d a to so total world uneasy called Thio 81 which is a green or times being hard. Plus, um, we know times peanut, Is we ready by two. So this gives us three or two. Be not be not. This is the total work done. Uh, from here, then we can find the heat. June. That is a quote from first law of thermodynamics changing internal energy plus work. Done. Curious change in Turner's before Mona Tommy cased the heavies C o r. Two uh, you know we know. Plus work we have is to you too, You know me not then combining these two waiting them. We get here on tree being old. He knows

And diagram so an autograph. It's more likely a diagram. And in the working I was told that I have to consider um on atomic ideal guest. That undergoes the fourth process showing the figure. So they were done by the gas positive negative or zero on the process A BBC Syrian to so I have to explain educated A. B beats the indeed the So in the process maybe we're saying that the heat is added and that yes it's working on the surroundings and are done by the gas is positive because it is working on this army in Bc we can see there is no change in volume. So There is no work doing the guest. So zero or so we're done by in process basically is you know in city we can see the volume is decreasing from there. We can see that and external agent is working on the Guest. So the work so work done by the guest is here is negative. Also same thing goes for process P A volume is decreasing here and it seems as an external agent is doing work on the guest. So that were done by the gas is also negative here. So these are the explanations and in uh number eight I was told if the heat added to the gas on process K. P. Is 27 june. So how much work? That's a guess. Hearing that process so and process a bee pressure is constant here, pressure is constant here. So we can say take your clothes too to change in the eternal and agenda data. So it added a 27 to So just 27 June To find the tw work done with the guessing falls through 27 see you. So this is the amount that I guess you work on it that sir.

This question we have a mono atomic gas, mono atomic gas and fully part of the question. The degree centigrade temperature has been doubled degrees centigrade temperature has been but we have to determine the internal energy to guess. Okay, so when I say for example, we have temperature even so this will be in the Calvin equals two plus 2 73. And if that double temperature is too even then it will be in the Calvin equals 2 to 7 plus 2 78. Say this is our X. And this is our by. So from here we can see that X is not equal to to access not sorry, we can write that. Why is not equal to two works. Okay. It is slightly less than the value. So we can are now the internal energy of mono atomic gas is this value? This is the internal energy. So from here we can see that you is directly proportional duty. So if this temperature is not has been doubled, then this internal energy will not get double. Okay so we can see that as the temperature has rised. So this internal energy will definitely rise but not by the factor too. So we can see that the internal energy of the guests will get mm will increase but increase but less than a factor of two. But less than a factor of two. Okay, so the correct answer is second option. Okay second option is correct. So this is the answer for the but the question. Okay, no moving to the part B in which we have data so in which we have temperatures Or even equals two 20 degrees integrate which is equals 2 to 93 Calvin. And we have temperature T two equals to 40 degrees integrate which is equals 2313 Calvin. Okay, so internal energy as we can see from the uh part a huge directly proportional to T. So we can write that you One by you to this will be equal to even by T two. So from here we can see that you do by Cuban this will be equals two T two but even so T two is equal to 313 Calvin and even is equals 2 to 93 Calvin. So from here after so when we get you to buy human equals to 1.7 Okay. So from here we can also see that when the degrees centigrade temperature is double then the uh internal energy is not about okay.


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