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Three moles of an ideal gas undergoes a reversible isothermal compression to one half its initial volume. Find the entropy change of the gas:Select one:2.1 J/K-2.1 ...

Question

Three moles of an ideal gas undergoes a reversible isothermal compression to one half its initial volume. Find the entropy change of the gas:Select one:2.1 J/K-2.1 J/K-17.3 J/K17.3 J/K

Three moles of an ideal gas undergoes a reversible isothermal compression to one half its initial volume. Find the entropy change of the gas: Select one: 2.1 J/K -2.1 J/K -17.3 J/K 17.3 J/K



Answers

Three moles of an ideal gas undergo a reversible isothermal compression at 20.0$^\circ$C. During this compression, 1850 J of work is done on the gas. What is the change of entropy of the gas?

Everyone is the problem. Baseball calculation off and profit changing and trophies defined us que appointing. Here it is given three moles often ideal gas is undergoing reverse of it. I shoot herbal compression. Okay, 1852 lover has to be done. We have to find the change in. And Proffy, Since it is ice, it'll process so changing Internal energy zero Applying first law of thermodynamics. Delta U minus two Blue This is zero's accuse cult toe minus W Oh, so Jewish culture You will get minus 1850 jewels on the preacher is given continually searches. That is to 93 Calvin So changing and trophy during the processes coupon T that is 1850 upon to 93. So it is to be minus six point driven. Julia Parker bit that son. Thanks for watching it

In this problem, we have one more of an ideal in mon atomic gas. And this gas is taken from this initial state with this initial pressure and volume to this finalist day with this pressure and this volume. And we want to compute what is the change in the entropy during the process. So let's consider a reversible process. And we're going to use the first law of thermodynamics and also these relations that we know for an ideal desk. So, uh from the first law of thermodynamics, uh, we can divide all this first law by the temperature. So doing that, we get in there left side of the equation this expression and then we have the differential change in the internal energy. That is yeah, given by this expression here sir. So he here we have N C B D. T divided by T. Because we are dividing all the equation by the temperature and then we have the pressure in the pressure. We can compute that pressure using this expression here. So we have instead of the pressure, N R. T divided by the boulder. Right. This is just the pressure. Also we have the differential change in the volume and also we have one temperature in the denominator because we are dividing all the questions by this temperature. So from here we see that we can cancel this temperature and we want to use this expression because this first term. It's just it's just the differential change in the entropy from the definition. So we want the change in the entropy not the differential but define it a change. We are just going to take the integral of all of this term. Right. So this is equal to the integral of N C B D T. If I didn't buy tea plus integral of And our mm the V. A divided by B. And this is uh this integral are taken from the initial state to the final state of the gas. Right. Okay. So in the first integral we can take is uh huh. C B. As equal to remember that for amman atomic gas. This is just three over to our So from here we have and three over to our these both terms are constant. So we can take that terms from out of the integral. And then we have the integral of GT divided by T in the second integral. Also we can take out of the integral. These values. We have this divisional advice. Okay. Also we know that the number of moles is just one. This is one more So this is one and this is one. Okay. And okay uh and these integrates here are just uh three over to our more also. And this integral is just the natural algorithm. So this is natural Lovering of this initial from this initial to this final state. So this is temperature the final state in this temperature at the initial state. Okay. And the second term is also the natural line but considering just the volume. Find the bottom and initial. Okay, all this information we have from the problem ah the final temperature and initial temperature mm We can't use the relation for the ideal gas. This relational game here in order to get the relation between the two temperatures. So from here the temperature from here the temperature is he has the pressure, the final pressure, the final volume divided by N. R. And the initial temperature is the initial pressure. The initial volume divided by our goals. Right? Yeah. And also we have this. Okay, so also remember that these are is the ideal gas constant. And we know the value of this are this is just eight 0.31. Okay, jules divided by mall. He killed me. Okay, so if we replace all the values that we have from here also we have the initial pressure and initial volume, the Final pressure and the final volume here, we must replace this initial by one. Right in final by two To replacing all this value which will get the answer. This answer is 18.4 and this is jules divided by Kirby. Okay, the mall here in the constant. This unit of mall is canceled because this and here is one more actually. Okay, so this council weighed the the small here in the er constant. Well this is the answer

We know that entropy change of the system is given by their that it was a just wish in one is that we need to find the beach you added or removed from the gas along this. We can find it by using the first law for more than that. There. That Eakins Tubman is it a little U minus? Nothing that the changing internal energy off the gas along this isil government, you know, is it was u minus the hand you It was this equation now from one to be therefore from abundant to begin their dynasty was WR one. It is a question Now we need to find the walking by the gas along. I took a word. Brutus. We know that the work done by the guests along this isil thermal protested W is a postal and Artie natural logo Final value divided by initial. Now the blue is with NRT natural logo one by a fight. Really one via what it indoors. But we know that in the Cuban be finally post will be won by five years. You can dental the value of the idea. Bigot. Look, there is a little NRP natural locals one opponent Fine. And delta is your postal NRT natural local one quantifies divided by we can cancel the illegal be here and we will get to their tires It goes through and not let your local one off. No. Built as a phone and is equipped are literally local one opponents by dividing both sides by and people get regarding both sides for envy Village it There s a couple And if it works it want 31 multiply natural logo one they get their dies upon and minus 13.4 minus 13 Want for rule park Ill the whole

So here we're going. Thio, evaluate the number of moles in this ice. So thermal process and I so thermal process denotes that the change in temperature will equal zero or weaken. Say temperature initial equals temperature final. And if this is the case, we can then say that the change in entropy would be equal to the number of malls times the ideal gas, constant times the natural log of the final volume divided by the initial volume. This is from Equation 20 four. Now, if we've solved for the number of moles and we find that N is equaling 20 2.0, divided by 8.31 the ideal gas constant times the natural log of the quotient of the volumes. So this will be 3.4 divided by 1.3 and we find that the number of moles there's going to be equal to 2.75 moles. This is our final answer. That is the end of the solution. Thank you for watching


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