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$\bullet$$\bullet$ Figure 15.35 shows a $p V$ diagram for an ideal gas in which its pressure tripled from $a$ to $b$ when 534 J of heat was put into the gas.(a) How much work was done on or by the gas between $a$ and $b ?$ (b) Without doing any calculations, decide whether the temperature of this gas increased, decreased, or remained the same between $a$ and $b .$ Explain your reasoning. (c) By how much did the internal energy of the gas change between $a$ and $b ?$ Did it increase or decrease? (d) What is the temperature of the gas at point $b$ in terms of the gas at point $b$ in terms of its temperature at $a, T_{a} ?$

Physics 101 Mechanics

Chapter 15

Thermal Properties of Matter

Temperature and Heat

The First Law of Thermodynamics

The Second Law of Thermodynamics

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Simon Fraser University

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This is chapter 15 Problem number 52. We've given a PV diagram for I for a guess, Um, and were given the fact that the pressure is tripled from as big warm from A to B. So the PV diagram shows a constant value as we go from a 0.8 to foreign be and were given the information that the pressure is tripled and 534 jewels off heat were put into this guest. So in part, they were asked to calculate the work done by or on the gas between a m. B. So we're asked for worked up. Now let's remember the professional work. Its gonna be pressured times. The change in the volume is you can look at this process. Actually, the volume is constant at all times. So if a volume is constant and doubt if he has to be zero right, it's the initial in the final. They're equal to each other. So you find miners be initial is gonna give us zero, therefore making it work. Zero equals now in our favor. Asked with that calculation, decide if the temperature is increased, decrease or remained constant as we go from A to B. So what happens to temperature His question here? So we know that this is an ideal gas sold. You can write the ideal gas law and our tea. Now we will get the to situations that we have pressure at point a involvement point A. What's going on is as we go from a to B Bali Miss Constant drive, it's not changing at all. They were not any any of gas to the system where we're not extracting any. Therefore, the number of Moses was a constant. So then, if we're tripling the pressure as we walked from a to B, we have to balance this out. That building south this equation right the fusion needs to hold. So the temperature has also triple. Based on this logic, which means the temperature has to increase right, T has to increase. Actually to be a precise. The temperature has to triple as well because the pressure is tripled right so you can say sins. P B equals three times initial and pressure at point A, then the temperature point B has to be three times the temperature of pointing. This is also our answer to party right if he noticed. No, it's pulled apart. See? And trying to answer that question in part C were asked, by how much did the internal energy of the gas change between A and B? So we're asked the internal energy and let's remember Hugh minus work that is gonna give us to change it. In terms of others, he always gets his. Our killer has given us 500 in dirty four jewels and the work that is zero. Then we have positive 534 jewels. As the change in the internal energy of this guess, which means internal energy of the gas is increased. Right, You seized by 534 jewels.

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