Answer:
2.87 liter.
Explanation:
Given:
Initially volume of balloon = 4.3 liter
Initially temperature of balloon = 350 K
Question asked:
What volume will the gas in the balloon occupy at 250 K ?
Solution:
By using:
![Pv =nRT](https://tex.z-dn.net/?f=Pv%20%3DnRT)
Assuming pressure as constant,
V∝ T
Now, let K is the constant.
V = KT
Let initial volume of balloon ,
= 4.3 liter
1000 liter = 1 meter cube
1 liter = ![\frac{1}{1000} m^{3} = 10^{-3} m^{3](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1000%7D%20m%5E%7B3%7D%20%3D%2010%5E%7B-3%7D%20m%5E%7B3)
4.3 liter = ![4.3\times10^{-3}=4.3\times10^{-3} m^{3}](https://tex.z-dn.net/?f=4.3%5Ctimes10%5E%7B-3%7D%3D4.3%5Ctimes10%5E%7B-3%7D%20m%5E%7B3%7D)
And initial temperature of balloon,
= 350 K
Let the final volume of balloon is
And as given, final temperature of balloon,
is 250 K
Now, ![V_{1} = KT_{1}](https://tex.z-dn.net/?f=V_%7B1%7D%20%3D%20KT_%7B1%7D)
![4.3\times10^{-3}=K\times350\ (equation\ 1 )](https://tex.z-dn.net/?f=4.3%5Ctimes10%5E%7B-3%7D%3DK%5Ctimes350%5C%20%28equation%5C%201%20%29)
![V_{2} = KT_{2}](https://tex.z-dn.net/?f=V_%7B2%7D%20%3D%20KT_%7B2%7D)
![=K\times250\ (equation 2)](https://tex.z-dn.net/?f=%3DK%5Ctimes250%5C%20%28equation%202%29)
Dividing equation 1 and 2,
![\frac{4.3\times10^{-3}}{V_{2} } =\frac{K\times350}{K\times250}](https://tex.z-dn.net/?f=%5Cfrac%7B4.3%5Ctimes10%5E%7B-3%7D%7D%7BV_%7B2%7D%20%7D%20%3D%5Cfrac%7BK%5Ctimes350%7D%7BK%5Ctimes250%7D)
K cancelled by K.
By cross multiplication:
![350V_{2} =4.3\times10^{-3} \times250\\V_{2} =\frac{ 4.3\times10^{-3} \times250\\}{350} \\ = \frac{1075\times10^{-3}}{350} \\ =2.87\times10^{-3}m^{3}](https://tex.z-dn.net/?f=350V_%7B2%7D%20%3D4.3%5Ctimes10%5E%7B-3%7D%20%5Ctimes250%5C%5CV_%7B2%7D%20%3D%5Cfrac%7B%204.3%5Ctimes10%5E%7B-3%7D%20%5Ctimes250%5C%5C%7D%7B350%7D%20%5C%5C%20%20%20%20%20%20%20%20%20%20%3D%20%5Cfrac%7B1075%5Ctimes10%5E%7B-3%7D%7D%7B350%7D%20%5C%5C%20%20%20%20%20%20%20%20%20%20%3D2.87%5Ctimes10%5E%7B-3%7Dm%5E%7B3%7D)
Now, convert it into liter with the help of calculation done above,
![2.87\times10^{-3} \times1000\\2.87\times10^{-3} \times10^{3} \\2.87\ liter](https://tex.z-dn.net/?f=2.87%5Ctimes10%5E%7B-3%7D%20%5Ctimes1000%5C%5C2.87%5Ctimes10%5E%7B-3%7D%20%5Ctimes10%5E%7B3%7D%20%5C%5C2.87%5C%20liter)
Therefore, volume of the gas in the balloon at 250 K will be 2.87 liter.