Having a lot of trouble in thermodynamics

[Tokimasa]

I've been having a lot of trouble in thermodynamics...are there any good sites that explain it? Here's my current problem:

Would I need to use the equation of state to solve this problem?

A cylinder contains oxygen at 20 degrees C, at a pressure of 15 atm and a volume of 12 L. The temperature is raised to 35 degrees C and the volume is reduced to 8.5L. What is the final pressure of the gas? Assume the gas is ideal.

I've been trying to use PV = nRT (P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvins). But that doesn't seem to be working out for me. But it would help to know if the number of moles varies based on the starting volume in liters or end volume in liters (using 1 mole = 22.4 liters).

The only other equation that even makes sense to me is V = V[0][1 + beta (T - T[0]) - k (P - P[0])]. But this is an ideal gas (well, you need to assume that it is) and you don't have beta or k to work with.

 

[whozum]

Thenumber of moles is constant, it says its ideal, so use theideal gas law

Solved for P

P_i = nRT_i/V_i

P_f = nRT_f/V_f

Equate the two, and cancel redundants (nR). They give you V_i, V_f, and T_f. This is enough to find P_f

 

[Tokimasa]

P = T/V
P[f] = T[f]/V[f]

How do you get there though? Do you just use PV = nRT twice or something? Or (PV)[1] = (PV)[2]?

 

[nomorevishnu]

very easy...
we know...P is directly proportional to T...
P is inversely proportional to V...

so P*V/T=constant...thus we come to the relation that P1*V1/T1=P2*V2/T2
in ur question P1 is given...T1 is given...V1 is given...T2 is given...V2 is given...
now what's the problem in finding P2...its very simple isn't it?
P2=P1*V1*T2/T1*V2...then u get the answer!

 

[Tokimasa]

OK. It's not P = V / T. It's P * V / T = constant? Or should there be parenthesis in there somewhere? And then the same with [f]s.

EDIT: What units to P, V, and T need to be in? Does P need to be in Pa or can I use atms? I'm guessing V must be in liters. Does T need to be degrees C or kelvins?

 

[Nylex]

Use SI units. V should be in m^3, T in K and P in N m^-2 (1 N m^-2 = 1 Pa and 1 atm = 10^5 Pa).

 

[whkoh]

If the initial and final pressures/volumes (except temperature, which must be in K) are the same, you need not convert to SI units. However, the question may require you to give the answer in SI units, in which case you have to convert.

 

[HallsofIvy]

Since the initial pressure is given in "atmospheres", unless there are direct instructions to the contrary, you should give the answer in "atmospheres". I would NOT recommend changing to SI units- although you DO need to use "degrees Kelvin"- PV= nRT assumes T= 0 at absolute zero! You don't need to know "n" or "R" or even "nR". As several people suggested, this is a simple proportions problem (provided you are careful about the temperature).

Since 0 C= 273.15 Kelvin, 20 degrees C is 293.15 K and 35 degrees C is 308.15 K. You are given, initially, that (15)(12)= nR(293.15) and, finally, (P)(8.5)= nR(308.16) where P is the final pressure you are seeking (in atmospheres). Divide one equation by the other to eliminate "nR" and solve for P.

 

[Tokimasa]

The answer must be in Pa. So I guess I should convert everything. The instructions are to have all answers in SI units unless the question directs otherwise, and there is nothing in the question that says the answer doesn't need to be in SI units.