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Question 3ptsConsider the following equation of state of a gas that slightly deviates from ideal gas behavior:P(V nb) nRTDetermine expressions for the following par...

Question

Question 3ptsConsider the following equation of state of a gas that slightly deviates from ideal gas behavior:P(V nb) nRTDetermine expressions for the following partial derivatives:@[email protected]=

Question 3 pts Consider the following equation of state of a gas that slightly deviates from ideal gas behavior: P(V nb) nRT Determine expressions for the following partial derivatives: @Dv @pr=



Answers

The pressure, temperature, and volume of an ideal gas are related by $P V=k T$, where $k>0$ is a constant. Any two of the variables may be considered independent, which determines the third variable. a. Use implicit differentiation to compute the partial derivatives $\frac{\partial P}{\partial V}, \frac{\partial T}{\partial P},$ and $\frac{\partial V}{\partial T}$ b. Show that $\frac{\partial P}{\partial V} \frac{\partial T}{\partial P} \frac{\partial V}{\partial T}=-1 .$ (See Exercise 67 for a generalization.)

So it has the equation of state P equals n R T. Over v minus N B. Want to take the partial derivative of this with respect two volume at constant temperature, folks. So um to take the derivative of this, this is this equal to negative and artie over the minus and B squared. And that's just from how you take derivatives. You can also take the partial with respect to temperature at constant volume. So now you treat the volume is constant And that's a sequel to end our over V -9b. Okay, so that's part a. Now we want to show that these mixed partial derivatives are the same. So if we take pressure and first take the derivative with respect to volume, then you get this. Now let's take the derivative of this with respect to temperature. Okay. And you would get negative and are over v minus N B squared. Yeah, let's take the derivative with respect to pressure. First you get this, then take the derivative with respect to volume of the answer to this, and you would get the same answer. These two are equal, therefore the mix partial derivatives are the same.

Problem. 69 Which an eight. Using that b is equal to okay, he Overbey and he is able toe B B over K and we is able to okay, be over peace. So we did that partial p fortune be is equal to fortune Fortune being off Katie over three, which is equal to negative. Katie over the square if it able to native over one day Katie Overview, which is able to negative he over over me meaty over d d is ableto the UK devi over d t is equal to que over over the So the foreign results from the port A So we get that fortunately fortunately, Fortunati punching the clients fortunately fortunate he is equal to negative. Really over v the over k Okay, over resource people can negative nothing more.

So any given question? We have, uh, the function off internal energy, which is the functional PVT. The bees preserve these volume and these temperatures off the gas. And they gathered all solving and our delicacy, Chris. And it's just he will be the second round, Harvey there and his number of moves an artist gas constant. So in our in and out with the constants. In part of the question, we have to find the partial derivative off you with B the win, sir, with respect to be and then the volume is enablement. So the release of year convinced of this like this be the in these independent the videos. This is relatable. We ve nt these air intermediate really was. And finally we have you which is dependent, do they? Even so, in order to find you my dp GAnderson stu by would be be be very dp stu by d v into t v by d. P. That's until your city todo Roditi. So that's been the And so in a worst case since, uh, t is an intimate ID variable. So Tekin Britain's BB by an r So do you by Levi with the energy you already be in tow? One. The Steve TV, do you? 1980? That's into the V very deeply. Since it is indifferent available, this will be zero first we have. Do you, Mary guilty go d de by dp Will the PBB in our this will be d u by d p That's d u the tv into zero. So the certainly come zero as indeed you very DT And so will be by in our so this survey quartile do you d be when more name is independent will be Do you wear dp does? Do you buy? Need to be by an r with this was God then in part of the of the West And we have to find out the uber duty when godliness independent So here the real lesson we can be established Earth's who he tedx These are independent Retrieve us PVT deserve interpretive! This is a cuckold. Yunus is dependent. He's in changeable. That's converged on us. Do you buy? Okay. The little people due to the u by D v b Bye the to Yes indeed. You buy indeedy in tow T t by DT. It should be so we can write be the Subaru Anarchy. So yeah, he is in temperature billions of years ago and not baby. So do you buy dp Toby? Be very it is. Do you do to off an artist 90. This gives you gv intuitive fever. DT, this will be settled still you going todo This is a quality you by DT in tow in our bi v This to you virginity to the both Do you buy duty involving is independent of the EU DP in our baby? Yes. Do you go deity? But this is the final answer and partly answered is this

So any given question? We have, uh, the function off internal energy, which is the functional PVT. The bees preserve these volume and these temperatures off the gas. And they gathered all solving and our delicacy, Chris. And it's just he will be the second round, Harvey there and his number of moves an artist gas constant. So in our in and out with the constants. In part of the question, we have to find the partial derivative off you with B the win, sir, with respect to be and then the volume is enablement. So the release of year convinced of this like this be the in these independent the videos. This is relatable. We ve nt these air intermediate really was. And finally we have you which is dependent, do they? Even so, in order to find you my dp GAnderson stu by would be be be very dp stu by d v into t v by d. P. That's until your city todo Roditi. So that's been the And so in a worst case since, uh, t is an intimate ID variable. So Tekin Britain's BB by an r So do you by Levi with the energy you already be in tow? One. The Steve TV, do you? 1980? That's into the V very deeply. Since it is indifferent available, this will be zero first we have. Do you, Mary guilty go d de by dp Will the PBB in our this will be d u by d p That's d u the tv into zero. So the certainly come zero as indeed you very DT And so will be by in our so this survey quartile do you d be when more name is independent will be Do you wear dp does? Do you buy? Need to be by an r with this was God then in part of the of the West And we have to find out the uber duty when godliness independent So here the real lesson we can be established Earth's who he tedx These are independent Retrieve us PVT deserve interpretive! This is a cuckold. Yunus is dependent. He's in changeable. That's converged on us. Do you buy? Okay. The little people due to the u by D v b Bye the to Yes indeed. You buy indeedy in tow T t by DT. It should be so we can write be the Subaru Anarchy. So yeah, he is in temperature billions of years ago and not baby. So do you buy dp Toby? Be very it is. Do you do to off an artist 90. This gives you gv intuitive fever. DT, this will be settled still you going todo This is a quality you by DT in tow in our bi v This to you virginity to the both Do you buy duty involving is independent of the EU DP in our baby? Yes. Do you go deity? But this is the final answer and partly answered is this


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