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

[TFM]

[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

$$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$

Thus

$$\frac{V_1*T_2}{T_1} = V_2$$

Thus $$V_1-V_2=\Delta V$$

The Attempt at a Solution

Converting the Temperatures into Kelvin, I get:

$$\frac{289.65*2.9}{306.65}$$

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

TFM

 

[astrorob]

What's the correct answer meant to be?

I can't see what's wrong with that!

 

[TFM]

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

 

[astrorob]

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..

 

[alphysicist]

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.

 

[astrorob]

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.

 

[alphysicist]

Hi astrorob,

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.

 

[astrorob]

Yeah my apologies, I've scanned the question without really reading it..Sorry TFM.

 

[TFM]

Ah, I see - we haven't covered that topic yet, I am getting ahead of myself.

Thanks,

TFM

 

[TFM]

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)

Thanks,

TFM