Gas expands adiabatically, find work.

[keith river]

An Ideal Diatomic Gas expands adiabatically, the temperature after expansion is 50 kelvin less than its original temperature. What is the work done by this gas?
Assume you have 0.5 kg of the gas. Molar Mass = 4

I already know the gas is helium but I don't think knowing what the gas is helps solve the problem :(

I know all the internal energy = Work as there is no heat energy.
I was going to try using W = Cv (dT)
But without the original temp it won't get very far.
I worked out no. of moles = 500 / 4 = 125
Also no. of molecules = 7.525x10^25
I can't find any relation without volume or pressure which could tell me original temperature.

Is there a way to find the original temperature or am I going in the wrong direction?

 

[Andrew Mason]

An Ideal Diatomic Gas expands adiabatically, the temperature after expansion is 50 kelvin less than its original temperature. What is the work done by this gas?
Assume you have 0.5 kg of the gas. Molar Mass = 4

I already know the gas is helium but I don't think knowing what the gas is helps solve the problem :(

That's a good thing, because it is not helium. Helium is monatomic.

I know all the internal energy = Work as there is no heat energy.
I was going to try using W = Cv (dT)
But without the original temp it won't get very far.

Why?

I worked out no. of moles = 500 / 4 = 125
Also no. of molecules = 7.525x10^25
I can't find any relation without volume or pressure which could tell me original temperature.
Is there a way to find the original temperature or am I going in the wrong direction?

You do not need to know the original temperature to determine the work done. All that matters is the change in temperature. (Hint: you were on the right track).

AM