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A gas at a temperature of $250 mathrm{~K}$ is contained in a closed vessel. If the gas is heated through $1{ }^{circ} mathrm{C}$, the percentage increase in its pre...

Question

A gas at a temperature of $250 mathrm{~K}$ is contained in a closed vessel. If the gas is heated through $1{ }^{circ} mathrm{C}$, the percentage increase in its pressure is nearly:(a) $0.4 %$(b) $0.6 %$(c) $0.8 %$(d) $1.0 %$

A gas at a temperature of $250 mathrm{~K}$ is contained in a closed vessel. If the gas is heated through $1{ }^{circ} mathrm{C}$, the percentage increase in its pressure is nearly: (a) $0.4 %$ (b) $0.6 %$ (c) $0.8 %$ (d) $1.0 %$



Answers

A gas at a temperature of $250 \mathrm{~K}$ is contained in a closed vessel. If the gas is heated through $1{ }^{\circ} \mathrm{C}$, the percentage increase in its pressure is nearly: (a) $0.4 \%$ (b) $0.6 \%$ (c) $0.8 \%$ (d) $1.0 \%$

Hi guys. Let's solve the problem. 5.22. We need to find the effect of the for being on the volume of one more off ideals we know for ideal guests For one mole of ideal guest, the relation between pressure volume and temperature is Revie by t. We're going to Constant. We'll be his pressure, resulting tease temperature. Therefore we can right? You want everyone, do you one? Then do lead to two. Very, very Tito. No. In this case, temperature decreases from 100. Okay with you, Stephen 2 400 This is Tito and the pressure is fixed so we can write the immigration. No, in the situation the pressures are same fixed, so weakened against them and we need to check Wanted. The volume becomes then we do it again too. We won my t one want to play Dwayne, You too. Let sense aren't the temperature revenues Therefore the boarding decreases by a factor of two for the same problem that m Parisian increases from 2 50 So since 2 500 citizens, we always need to convert the solutions to building leads to the revolution. We need to just turned 73 which gives us 5 23 Children and for 500 gives us 7 73 Children. And here this is Steven. And this is did you and begin The equation is re to it. Well too, everyone by anyone want to paint by Tito because he is fixed. So he's not included here. We won by mid since Aunt Oh, doing a victory. I want to play by 7 73 killings, which gives us one point for a want to plan for everyone. Therefore, the final volume increases were factor off one point for eight intended trees ISS for question one. No, awful. We shall see or fish in sea. Done. Temperature is fixed, but the pressure is changing from to him It used to be one to six city in which is we do. And now we know we won. We won by Do you want to we to be two by two? Because the temperatures are fixed so we can write. You want the only calls to be true from here. We need to get we do, which is? He won't be won by two. The one is too me to Chrissy there's more William Decreases way three minutes

Problem, 65 says that it containers filled with an ideal gas to a pressure of 11 atmospheres and a temperature of zero degrees Celsius or 273 killed him. So part a of this problem asks what the pressure in the container would be if it's heated to 45 degrees Celsius. So this really seem like much information is given by this problem. But the's er parts A, B and C well easily are easily solved by the simple relationship that, um, the pressure and temperature of a gas are quarterly ahead such that the initial pressure and temperature is, um, equal thio the ratio of the final or, um, pressure and temperature so we can do then, is they can fill in the original, um, the original information given by the problem. And of course, we have to use the Calvin here because you can't divide by zero, and then we can solve for the final pressure or this pressure of, um, you know, uh, be system here, Um, after converting this 45 degrees Celsius to Calvin Suite 318 coven, it can plug that and problem here, and this gives us that um, the final pressure for the pressure of the system. Given these given these conditions as 12.8 atmospheres, remember that you can just cross, multiply, um, and then solve for B so I can do the same thing for parts B and C here. Um, we can do this same relationship. So 11 atmospheres over 273 calvin for are sort of starting condition. Um, we have any pressure and they want to solve for the new temperature so insulting for a new temperature, we get 161 Calvin or a negative 112 degrees Celsius. Finally, you can do the same thing for part C. Here again, we have a new pressure than it wants us to solve for a final temperature here so you can plug in the same sort of information to solve for our final temperature. And during the same kind of math that we just did in part B, um, we get 620 Calvin or 347 degrees Celsius

Question number nine. It's also in reference to Boyle's law, where we are relating the pressure of a gas to the volume of a gas keeping temperature constant and the number of moles of the gas constant first were given a cylinder. It is that has a piston that can move up and down. Originally, the piston is set to 500 mL. The gas has a pressure of one atmosphere, and the temperature of the gas is 300. Kelvin. If we were to pull up the piston and increase the volume to a total of 1000 mL, we're going to have to cut the pressure in half. If the temperature stays constant at 300 Kelvin and the number of gas molecules stay constant. This is according to Charles Flaw, Oops, Boyle's Law Charles Laws Volumen temperature. Boyle's law states that for gas at constant temperature and constant number of moles, the pressure times the volume is equal to a constant. So if I just increase the volume if I doubled the volume, I'm gonna have to cut the pressure in half in order to have this product stay constant

In this question, I'm going to use the equation. P times V equal to end times are times t because we have an ideal guess S O in the first part, you want to find the volume. Volume is equal to, uh, n times are times t divided by field and I'm going to substitute what is given in the question and is two times are, which is 8.314 times T, which is 250 divided by Pete, which is 1.5 times 10 to the five. Ah, Pascal. And this will give me 0.0 27 meter Cute. Knowing the second part you want to find a temperature temperature is equal to p times V, divided by and times are no pressure is four times 10 to the five times volume is half of what God in the last part. So it's 0.0 27 divided by two divided by n. That is a still two times are that is 8.314 and that this gives me 330 killed


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