How much additional ethanol can be stored in a cooled steel tank?

In summary: The correct answer is that the volume of ethanol that can be put into the tank after it has been cooled to 16.5 degrees Celsius is 2.739 metres cubed.
  • #1
TFM
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[SOLVED] Gas Laws Problem

Homework Statement



A steel tank is completely filled with 2.90 metres cubed of ethanol when both the tank and the ethanol are at a temperature of 33.5 degrees Celsius.

When the tank and its contents have cooled to 16.5 degrees Celsius, what additional volume of ethanol can be put into the tank?


Homework Equations



[tex]\frac{V_1}{T_1} = \frac{V_2}{T_2} [/tex]

Thus

[tex] \frac{V_1*T_2}{T_1} = V_2[/tex]

Thus [tex]V_1-V_2=\Delta V[/tex]

The Attempt at a Solution



Converting the Temperatures into Kelvin, I get:

[tex]\frac{289.65*2.9}{306.65}[/tex]

This gives a volume of 2.739, and a change in volume of 0.16, but apparently this is incorrect?

TFM
 
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  • #2
What's the correct answer meant to be?

I can't see what's wrong with that!
 
  • #3
I'm using Mastering Physics, so it doesn't tell you what the answer should be!

The volume is given in metres cubed, and wanted in meters cubed, I've converted the temperature in Kelvin, so I can't see why it says the answer us wrong?

TFM
 
  • #4
Personally I don't see what's wrong with your answer - I'm wondering whether mastering physics has incorrectly worked it out without converting to K or maybe it's taking 0 celsius to be 273 K and not 273.15? I don't really know how mastering physics works..
 
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  • #5
Hi TFM,

The equations you are using describe an ideal gas. I think what you need here is the equations describing thermal expansion (and contraction) of solids and liquids. Each material has an expansion coefficient, so you'll need to track how much the tank shrinks in volume as well as how much the ethanol shrinks in volume.
 
  • #6
alphysicist said:
Hi TFM,

The equations you are using describe an ideal gas. I think what you need here is the equations describing thermal expansion (and contraction) of solids and liquids. Each material has an expansion coefficient, so you'll need to track how much the tank shrinks in volume as well as how much the ethanol shrinks in volume.

Can't dispute that.. but wouldn't have thought that to be taken into consideration if the coefficient wasn't given.
 
  • #7
Hi astrorob,

astrorob said:
Can't dispute that.. but wouldn't have thought that to be taken into consideration if the coefficient wasn't given.

I not understanding what you mean. What wouldn't need to be taken into consideration? My point was that it's not correct to use the ideal gas law for the contraction of solid steel and liquid ethanol.
 
  • #8
Yeah my apologies, I've scanned the question without really reading it..Sorry TFM.
 
  • #9
Ah, I see - we haven't covered that topic yet, I am getting ahead of myself. :rolleyes:

Thanks,

TFM
 
  • #10
Yeah, yu get the right answer using the Thermal Volume Expansion Equations (The coefficient values are given in the textbook that goes with Mastering Physis - You can get MP without the book, then you do have a problem:rolleyes:)

Thanks,

TFM
 

FAQ: How much additional ethanol can be stored in a cooled steel tank?

What are gas laws?

Gas laws are a set of mathematical relationships that describe the behavior of gases under different conditions, such as pressure, temperature, and volume.

What are the different types of gas laws?

The three main types of gas laws are Boyle's Law, Charles's Law, and Gay-Lussac's Law. Boyle's Law describes the relationship between pressure and volume, Charles's Law describes the relationship between temperature and volume, and Gay-Lussac's Law describes the relationship between pressure and temperature.

What is the ideal gas law?

The ideal gas law is a combination of Boyle's Law, Charles's Law, and Gay-Lussac's Law, and is written as PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature.

How do I solve gas law problems?

To solve gas law problems, you will need to know the values of three of the variables (P, V, n, or T) and use the appropriate gas law equation to find the fourth variable. It is important to make sure all units are consistent and to use the correct units for the gas constant, which can vary depending on the units used for pressure, volume, and temperature.

What are some real-life applications of gas laws?

Gas laws have many real-life applications, such as predicting the behavior of gases in weather systems, understanding the function of scuba diving equipment, and determining the proper conditions for storing and transporting gases in industries such as medicine and manufacturing.

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