Question
Suppose you fill a huge black plastic bag with 413.9 L of air ona sunny day, when it's 26.4 degrees C outside. You tie the bag off,and the black plastic material is very thin, so the bag starts toheat up due to the sunlight. It expands so much that it begins tofloat up into the sky. The air in the bag expands because of theheat to a volume of 475.1 L. What must be the new Celsiustemperature inside the bag?
Suppose you fill a huge black plastic bag with 413.9 L of air on a sunny day, when it's 26.4 degrees C outside. You tie the bag off, and the black plastic material is very thin, so the bag starts to heat up due to the sunlight. It expands so much that it begins to float up into the sky. The air in the bag expands because of the heat to a volume of 475.1 L. What must be the new Celsius temperature inside the bag?
Answers
A weather balloon is filled to the volume of $135 . \mathrm{L}$ on a day when the temperature is $21^{\circ} \mathrm{C}$. If no gases escaped, what would be the volume of the weather balloon after it rises to an altitude where the temperature is $-4^{\circ} \mathrm{C} ?$
Chapter 11 Problem 24 asks about the relationship between pressure and temperature, so we'll remember that that formula is P one over. T one is equivalent to P two over t two and we can rewrite this. Has p won t to equals p two t one. Now this equation asks us to solve 42 so we can rewrite this as t two is equivalent to p two t one over p one. One final thing to keep in mind is in this equation. We need all of our temperatures to be expressed in the Kelvin units. So first will converge all of our Celsius temperatures to help it. And the question asks us to give our final in certain degrees Celsius. So at the end, we will convert back. So let's go ahead and evaluate this. So we're given RP two as to a T M and our initial temperature as 200 Calvet or initial pressure was one a t. M. So we can evaluate this out to 400 Kelvin No, we convert this back to Celsius, will subtract 2 73 and that gives us our final answer of 127 degrees Celsius.
Hello Today we're going to talk about Chapter 12 Question 42 which tells us about a balloon that we get feel filled with helium. Nice, shiny red balloon and it's filled with helium toe, a volume of 2.30 leaders. Now the temperature outside is about 311 Kelvin. So it's a pretty warm day. We've got, you know, our son here just kind of being warm and sunny and heating up our balloon. And so we take the balloon inside to a new temperature of 295. Kelvin. It's about room temperature. Were asked what happens to the volume of the balloon. And so if we set up Charles is Law V one over T one is equal to V two over tea, too. We have the initial volume and the two temperatures which Aaron, Kelvin and so we can solve for the new volume. This gives us rearranged V one. T two over t one equals V two, and now we can just plug in our numbers. 2.30 leaders times 311. Kelvin. Excuse me. Not 311. Kellan. Our new temperature is 295 Kelvin, divided by our old temperature, which is 311 Kelvin. And so when we bring the balloon inside, it shrinks to about 2.18 leaders. If we put this into our calculator, so we might not notice it. But taking balloons between areas of different temperature will genuinely affect the size of the balloon. We just might not perceive it. You'd extreme temperature differences to notice. Thank you.
So to solve this problem, we're going to use Charles's law be one over T1 equals V two over T two. And we are solving for the new volume V two. So we would just multiply both sides by T two. So V two is able to T two times we want over T. one. Now let's convert the temperatures first to Calvin. T one is 26°C,, and T two is 21°C.. So we have to add 273 to both of these numbers. 26 plus 273 is 299 and then 21 plus 2 72 is five. Less than that. So 2 94 Calvin. Okay, so V two is going to be the second temperature 2 94, Calvin Times the original volume, which is 0.82 leaders And then divided by the second, the first temperature which is 299. So that comes out to zero 806 which is 0.81 leaders wanted to do significant figures. So very slight decrease in volume because of the slight temperature decrease
In this problem, given that the physical too 14 F, we all know that this is equal to five by nine multiplication and t f minus 32 C suggest putting the value of TF here. I can like five by nine multiplication, 40 minus 32 which is equal to 40 by nine. Now going forward and simplifying this problem for that. So according to Charles's law, I can be by T K. Is equal to be death by EKGs, not hear cicadas in the final temperature in Calvin the cage. Original temperature in kelvin and peter's his final volume. He'd original volume. So calculating the value of DK desk which is equal to be this multiplication. PK by B decade s is the final temperature in kelvin. So just putting the value 36 liter multiplication to 7 7.44 Calvin by He's given us 26 liter. So this value this value get cancel out. And finally I get the value of cadiz is equal to 38 4.147 Kelvin. So the Calvin temperature charge needed. The Calvin temperature charge needed he needed is equal to take this that is 384.147 277 44, which is equal to €1 Calvin as the answer.