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$\bullet$$\bullet$ Assume that the gases in this problem can be treated as ideal over the temperature ranges involved, and consult Appendix $\mathrm{C}$ to determine the necessary molar masses.(a) How much heat isneeded to raise the temperature of 75.0 g of $\mathrm{N}_{2}$ from $12.1^{\circ} \mathrm{C}$ to $49.5^{\circ} \mathrm{C}$ at constant volume? (b) If instead you want to produce the same temperature change in 75.0 $\mathrm{g}$ of $\mathrm{O}_{2}$ at constant volume, how much heat do you need?

a) $2081.23 . \mathrm{J}$b) $1822 . \mathrm{J}$

Physics 101 Mechanics

Chapter 15

Thermal Properties of Matter

Temperature and Heat

The First Law of Thermodynamics

The Second Law of Thermodynamics

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Lectures

03:15

In physics, the second law of thermodynamics states that the total entropy of an isolated system can only increase over time. The total entropy of a system can never decrease, and the entropy of a system approaches a constant value as the temperature approaches zero.

03:25

The First Law of Thermodynamics is an expression of the principle of conservation of energy. The law states that the change in the internal energy of a closed system is equal to the amount of heat energy added to the system, minus the work done by the system on its surroundings. The total energy of a system can be subdivided and classified in various ways.

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this's Chapter 15. Problem number 36. In part, they were asked how much heat is needed to raise the temperature of 75 grams of nitrogen. Yes, from an initial temperature of 12.1 cells. Use to a final temperature ofthe 49.5. Cell sees Acosta William. Since we're asked to calculate the heat, let's remember the amount of heat is proportional to the number of moles that we have times the heat capacity, right? The mueller he capacity, times the temperature difference now, since for directly not we're not directly given the number of moles guests that we have, we have to calculate that. And also we need to calculate the more he capacity since for dealing with the dark comic gas. As you know, the Mueller he capacity is going to be 5/2 times. Our universe is if he had one of them. I guess it was you. You remember he was three House stands are. But since we have data to make, this is we're related Now, in order to calculate the number of moles, then what we have is the mess. The total mass right equals two number of most times the mauler, miss. So then if we divide both sides by the molar mass, we get number moles equals who talk of to the mass divided by the mauler mass for nitrogen. Right, So we can put this this equation in the heat equation. So then, well, if you're looking at something like total mass divided by the mall a mass of nitrogen times five over two times are times doubt fatigue. Right? So now we're given all the information here so we can calculate the amount of heat. This is R A. Now the mass is 75 grams. Let's convert that two kilograms and then we have five and then we have the gas constant 8.315 jewels Permal, Calvin and we have Delta teeth. So as faras, the difference in temperature is concerned. You know that in this equation we need to talk. We need to write the temperature in Calvin Have everyone we've taken. A difference really is not going to matter because initial temperature is going to seven and three plus 12.1, which is 285.1 Calvin. And the final is going to be 2 73 6 were having the same number two. Both. It's not going to change. What about Tha T is, I guess, is what I'm trying to explain you here. So the difference. 325 dude, if friends doubt the tea is still 37 point for, which would be cool to 49.5 minus 12.1 anyways. But yeah, we did the conversion. Let's let's use this. The end. We can put 37 point for Calvin here, and we're going to divide this by the mall. A vassal of nitrogen Adam Oh is what 14 point series of seven freaking amount of light by two right, which would be grams per long. So let's convert that to kill of grams for mold. And we also have a two here. And denominator, let's not forget back. So we're butt plug in the numbers what we have for the amount of heat that the nitrogen guests would need, you know, it should change this temperature from 12.12 40. Number five is 2000 and 81. Jules, all right now in part B, everything else is constant. Still, we have the same mass the same initial and finer temperatures have ever. Now we're dealing with oxygen. So what happens if we have oxygen instead of nitrogen? What would change if we were to calculate the heat again? Let's let me take you back to this heat equation Mass divided by molar mass. Okay, so the molar mass is going to change for sure, right. But the rest is pretty much going to remain the same If the Mueller he capacity is going to stay the same because we're still dealing with for the atomic guess. Now, then M times five are delta t over more mess this time. It's off the oxygen, and we have a two here now. 75 grams Time center were negative. Three kilograms times five times 8.315 Jules, for more Calvin times the temperature. Radiant. Right? 37.4. Calvin, divide this by now. The moments of oxygen. We can look this up, but it is plus 16 grams per All right. So now, uh, let me They didn't. And that's the way. My apologies. So now, times two, when we do the calculation, we're going to see that we need 18. 22 Jules, less. Um, heat right

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