Bizarre Atmospheric Physics Problem

[Daniel Sellers]

Homework Statement

For an atmospheric physics class, we are given this problem that I and a classmate have been struggling with for days. Reaching out here for some help.
Full Problem statement in the image attached.

We have a balloon at 293 K and 101,300 Pa. How much fuel is needed to raise the balloon to a pressure of 90,000 Pa if the fuel gives 5*10⁷ J/kg. The Balloon expands adiabatically while rising.

That's all the information we're given accept that the answer should be about 5 kg (or 2.5 * 10⁸ J)

Homework Equations

Perhaps the adiabatic work condition? But that involves volume.

c_p*m*ΔT = Q but I can't see how to solve for the air mass

The Attempt at a Solution

I have tried everything I can think of. My professor's only response has been to say I should solve for the final temperature first, which he says should be about 360 K. I can't get this value. But even if I take it as a given I can only solve the final density, not the actual mass and therefore not an amount of energy.

Every route I try hits a wall where I need a volume or an air mass to obtain an energy value.

Can anyone suggest a way to solve for the energy required without knowing the mass or at least the volume of the balloon? Going kind of crazy with this problem. It's due in two days and there are midterms to study for. Any help is appreciated.

 

[Chestermiller]

It seems like there is information missing like the amount of air in the balloon or the balloon diameter.

 

[BvU]

My idea would also be that for a bigger balloon more energy would be needed...

 

[Daniel Sellers]

Ok, thanks for saying so cause I was starting to feel like I was going crazy.

Can anyone at least posit how one would solve for the final temperature inside the balloon? Because then I could solve for a final density and at least say I did something.

I am as annoyed and frustrated as I have ever been in a class. Thanks for your help

 

[Chestermiller]

Ok, thanks for saying so cause I was starting to feel like I was going crazy.

Can anyone at least posit how one would solve for the final temperature inside the balloon? Because then I could solve for a final density and at least say I did something.

I am as annoyed and frustrated as I have ever been in a class. Thanks for your help

You would use the equations for an adiabatic reversible expansion.

 

[Daniel Sellers]

You would use the equations for an adiabatic reversible expansion.

Not to be difficult, but don't all of the equations for adiabtic processes involve volume?

You have already said that this problem seems to be missing information, so if that's true please feel don't feel obligated to repeat yourself

 

[haruspex]

at least say I did something.

You could start from the answer and work back to deduce the initial volume.
Prof can then check that against the omitted data.

 

[Daniel Sellers]

If anyone was interested in knowing the answer to this problem;

My professor forgot to include the critical data of volume and mass. He added the missing info the day before it was due, then he gave a condescending lecture to the class about how we all just want to plug things into equations and not really think about the problem.

So that's cool. Thanks for everyone's replies