Answer:
0.714 liter.
Explanation:
Given:
The balloon initially has a volume of 0.4 liters and a temperature of 20 degrees Celsius.
It is heated to a temperature of 250 degrees Celsius.
Question asked:
What will be the volume of the balloon after he heats it to a temperature of 250 degrees Celsius ?
Solution:
By using:
![PV=nRT](https://tex.z-dn.net/?f=PV%3DnRT)
Assuming pressure as constant,
V∝ T
Now, let K is the constant.
V = KT
Let initial volume of balloon ,
= 0.4 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)
0.4 liter = ![0.4\times10^{-3}=4\times10^{-4} m^{3}](https://tex.z-dn.net/?f=0.4%5Ctimes10%5E%7B-3%7D%3D4%5Ctimes10%5E%7B-4%7D%20m%5E%7B3%7D)
And initial temperature of balloon,
= 20°C = (273 + 20)K
= 293 K
Let the final volume of balloon is ![V_{2}](https://tex.z-dn.net/?f=V_%7B2%7D)
And a given, final temperature of balloon,
is 250°C = (273 + 250)K
= 523 K
Now,
= ![KT_{1}](https://tex.z-dn.net/?f=KT_%7B1%7D)
![4\times10^{-4}=K\times293\ (equation\ 1 )](https://tex.z-dn.net/?f=4%5Ctimes10%5E%7B-4%7D%3DK%5Ctimes293%5C%20%28equation%5C%201%20%29)
= ![KT_{2}](https://tex.z-dn.net/?f=KT_%7B2%7D)
![=K\times523\ (equation 2)](https://tex.z-dn.net/?f=%3DK%5Ctimes523%5C%20%28equation%202%29)
Dividing equation 1 and 2,
![\frac{4\times10^{-4}}{V_{2} } =\frac{K\times293}{K\times523}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Ctimes10%5E%7B-4%7D%7D%7BV_%7B2%7D%20%7D%20%3D%5Cfrac%7BK%5Ctimes293%7D%7BK%5Ctimes523%7D)
K cancelled by K.
By cross multiplication:
![293V_{2} =4\times10^{-4} \times523\\V_{2} =\frac{ 4\times10^{-4} \times523\\}{293} \\ = \frac{2092\times10^{-4}}{293} \\ =7.14\times10^{-4}m^{3}](https://tex.z-dn.net/?f=293V_%7B2%7D%20%3D4%5Ctimes10%5E%7B-4%7D%20%5Ctimes523%5C%5CV_%7B2%7D%20%3D%5Cfrac%7B%204%5Ctimes10%5E%7B-4%7D%20%5Ctimes523%5C%5C%7D%7B293%7D%20%5C%5C%20%20%20%20%20%20%20%20%20%20%3D%20%5Cfrac%7B2092%5Ctimes10%5E%7B-4%7D%7D%7B293%7D%20%5C%5C%20%20%20%20%20%20%20%20%20%20%3D7.14%5Ctimes10%5E%7B-4%7Dm%5E%7B3%7D)
Now convert it into liter with the help of calculation done above.
![7.14\times10^{-4} \times1000\\7.14\times10^{-4} \times10^{3} \\0.714\ liter](https://tex.z-dn.net/?f=7.14%5Ctimes10%5E%7B-4%7D%20%5Ctimes1000%5C%5C7.14%5Ctimes10%5E%7B-4%7D%20%5Ctimes10%5E%7B3%7D%20%5C%5C0.714%5C%20liter)
Therefore, the volume of the balloon be after he heats it to a temperature of 250 degrees Celsius is 0.714 liter.