- #1
mateomy
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Two moles of a monatomic ideal gas are at a temperature of 0°C and a
(dQ = 0) and quasi-static volume of 45 liters. The gas is expanded adiabatically
until its temperature falls to - 50°C. What are its initial and final pressures and its final volume?
I've been beating my head against a wall for a while now on this one.
I know how to find the initial pressure. That's just an easy PV=nRT problem. I get an answer of 100,956 Pa (0.1MPa). I can't find the final pressures though, totally stuck.
So what I've done thus far is to utilize the first law in that I know dQ = 0. So I know that dU = -dW. Solving the U = cNRT for initial and final temperatures and taking the difference, I get an energy which I know must be attributed to the work done. This is where I get stuck.
Not sure what steps to take next. Need some assistance, thanks.
I thought I could try
[tex]
W = - \int PdV
[/tex]
which I could do some substitution to get to (eventually),
[tex]
W = -nRTln\left(\frac{V_f}{V_i}\right)
[/tex]
But when I do that and I set W to the difference in energy I found earlier, I get an answer that doesn't match my book's.
(dQ = 0) and quasi-static volume of 45 liters. The gas is expanded adiabatically
until its temperature falls to - 50°C. What are its initial and final pressures and its final volume?
I've been beating my head against a wall for a while now on this one.
I know how to find the initial pressure. That's just an easy PV=nRT problem. I get an answer of 100,956 Pa (0.1MPa). I can't find the final pressures though, totally stuck.
So what I've done thus far is to utilize the first law in that I know dQ = 0. So I know that dU = -dW. Solving the U = cNRT for initial and final temperatures and taking the difference, I get an energy which I know must be attributed to the work done. This is where I get stuck.
Not sure what steps to take next. Need some assistance, thanks.
I thought I could try
[tex]
W = - \int PdV
[/tex]
which I could do some substitution to get to (eventually),
[tex]
W = -nRTln\left(\frac{V_f}{V_i}\right)
[/tex]
But when I do that and I set W to the difference in energy I found earlier, I get an answer that doesn't match my book's.