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Physics 101 Mechanics

1 week, 5 days ago

A balloon contains 3.9 liters of nitrogen gas at a temperature of 84 K and a pressure of 101 kPa. If the temperature of the gas is allowed to increase to 28°C and the pressure remains constant, what volume will the gas occupy?

Indiana University Bloomington

Answer

A gas has a volume of $3.86 \mathrm{~L}$ at $45^{\circ} \mathrm{C}$. What will the volume of the gas be if its temperature is raised to $87^{\circ} \mathrm{C}$ while its pressure is kept constant?

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Video Transcript

Hello. This is problem No. In this problem, we have a sample of gas um, and it is remaining constant. It's the same sample of gas. So the number of moles is constant. We're also told that the pressure is constant. However, we see that the temperature and volume are changing. So that tells us this is a Charles law problem. Charles Law says that volume and temperature are directly proportional when pressure and number of moles are kept constant. So the equation for Charles Law is V one over T one equals V two over T two. And the temperature, in order for this equation to work, the temperature must be the absolute temperature or in other words, it must be in kelvin. All right. So let's list out our variables here, V one, T one, V two and T two and figure out what these are from the problem and what it is we're looking for. So, the problem tells us that we have 3.86 leaders initially, And that's what our view one in T one are are the initial conditions. The initial temperature is 45°C.. I am going to immediately change that to kelvin By adding 273 and that gives me 318 killed in V two is what we're solving for T two Is 87°C.. Changing that to Kelvin. We had 2 73 and we get 360 Calvin. Right now we can plug these into the equation and solve for V two. So, we have three 86 liters Over 318, Kelvin Is equal to V two, which is what we're looking for. Divided by 360 Kelvin. Yeah, Solving for V two and rounding into three significant figures. Since all of our values have three significant figures, Gives us 4.37 leaders. All right, That would be our final answer. Yeah. Remember it's a direct proportion for Charles law. So since the temperature increased, we would expect the volume to also increase. And this answer supports that Yeah.