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Eugene S.
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Problem 48 Easy Difficulty

A gas is compressed from an initial volume of 5.55 L to a final volume of 1.22 L by an external pressure of 1.00 atm. During the compression the gas releases 124 J of heat. What is the change in internal energy of the gas?

Answer

$$
\begin{aligned} \Delta E &=q+w \\ &=-124 J+(438.74 J) \\ &=314.74 J \end{aligned}
$$

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Video Transcript

So in this problem, we're told that a gas ah compresses from five point five five leaders toe one point two two leaders. Actually, it expands from one point to two leaders to five point five five leaders with an external pressure of one atmosphere and a heat of one twenty four jewels being released. And we want to find the change in internal energy. Delta E. And so we use the first law of thermodynamics. Delta E equals heat Q Plus work W Our cue is given. And since it's Heat released its negative as one twenty four Jules and we can solve for R W by using P Delta V. And so we know our work is positive, since the surroundings are doing work on the system and so we can just plug in our values here one point zero zero atmospheres and then our change in V will be five point five five, minus one point two two. That gives us four point three three leader atmospheres, and we want to convert this into jewels so we multiply by the conversion factor. One a one point three to five Jules per leader atmosphere, and that gives us four thirty eight point seven jewels. And so now we just return to our original equation. Tell T E equals Q Negative one twenty four Jules Plus W for thirty eight point seven jewels, and that gives us a final answer of three hundred fifteen Jules rounded two three six things, and so that will be our change in internal energy of the system.

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