Thermodynamics

[25thhour]

Hey guys, I am having trouble with some stupid thermodynamics questions...

I don't know what formulas to use and its kinda frustrating. I can't derive them.

1. The figure shows a 50-kg frictionless cylindrical piston that floats on 0.68 mol of compressed air at 30°C. How far does the piston move if the temperature is increased to 300°C? The piston is 10cm long. I have done this one countless times and I keep getting 311cm as a change in height.

mgh = nRT
is the formula I use and I do it twice and subtract what I get at 573K from what I get at 303K. This is really frustrating me.

2.
The figure (not to scale) shows a pV diagram for 1.8 g of helium gas (He) that undergoes the process 1 → 2 → 3. Find the value of V3. The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K, and the atomic weight of helium is 4.0 g/mol.

At point 1
P1 = 2 ATM
T1 = 37 C
V1 = ?

At Point 2
P2 = ?
T2 = 657 C
V2 = V1 = ?

At Point 3
P3 = P1 = 2ATM
T3 = ?
V3 = ?

I am totally lost on this one... I have tried to make equations to find one of the missing variables for P3 but failed I basically just keep ending up with this equation.

(2atm)V3 = (.036945)(T3) Have tried solving many times but end up with

xV3 = yV3


3. A cubical box, 5.00 cm on each side, is immersed in a fluid. The pressure on the bottom surface is 539 Pa higher than the pressure on the top surface. What is the density of the fluid?

Ya so I have gotten to the answer 11000N/m^3
But thats not density...

Will give credits to whomever helps me

[Zapmeister]

disclaimer: i haven't done this stuff in years.

1.

PV = nRT is the relevant equation. so:

the only thing you're changing is T, and the thing that's going to change is V. P,n,R are all constant here.

so: V2/V1 = T2/T1 = 573/303
since the height you started with is proportional to volume, have h2/h1 = 573/303
so h2 = 573/303*10cm = 18.9cm
so h2-h1 = 8.9cm.

i'm pretty sure all the other numbers in the question are irrelevant.

2.

um. i don't think this is doable unless there's extra information in the diagram that you didn't tell us. your equation "(2atm)V3 = (.036945)(T3)" is correct, there's no way to explicitly get V3 and T3 from here (like what's to stop the answer from being T3=T1 and V3=V1?)

to get V1,V2,P2 you can use PV = nRT like you're trying to do for V3, which i guess you've already done.

3.

pressure difference = density * g * height difference

539 N/m^2 = density * 9.8 N/kg * 0.05m
density = 539/(9.8*0.05) kg/m^3 = 1100 kg/m^3 which suggests your answer would have been right except that you left out g in the formula.

[25thhour]

Originally Posted by Zapmeister

disclaimer: i haven't done this stuff in years.

1.

PV = nRT is the relevant equation. so:

the only thing you're changing is T, and the thing that's going to change is V. P,n,R are all constant here.

so: V2/V1 = T2/T1 = 573/303
since the height you started with is proportional to volume, have h2/h1 = 573/303
so h2 = 573/303*10cm = 18.9cm
so h2-h1 = 8.9cm.

i'm pretty sure all the other numbers in the question are irrelevant.

2.

um. i don't think this is doable unless there's extra information in the diagram that you didn't tell us. your equation "(2atm)V3 = (.036945)(T3)" is correct, there's no way to explicitly get V3 and T3 from here (like what's to stop the answer from being T3=T1 and V3=V1?)

to get V1,V2,P2 you can use PV = nRT like you're trying to do for V3, which i guess you've already done.

3.

pressure difference = density * g * height difference

539 N/m^2 = density * 9.8 N/kg * 0.05m
density = 539/(9.8*0.05) kg/m^3 = 1100 kg/m^3 which suggests your answer would have been right except that you left out g in the formula.

Thanks. But for number 2. The only possible answers are
120 cm
1300 cm
250 cm
130 cm... :S

And the pV diagram, 2-3 is a isotherm

[Zapmeister]

for question 2, "isotherm" means the temperature stays the same, so T2 = T3 = 657c, then just use PV=nRT

i think those answers you listed were for question 1 not 2... in that case... um... i don't know. i don't think it would really make sense for the height to increase that much

[25thhour]

Yes they were, I keep getting the answer 311cm. I dunno why.