I do not know if I am allowed to have two question in one post, so forgive me if I am breaking a rule. These two are frustrating me as I cannot see where the error in my process is.
1) A 1.00-mol sample of an ideal diatomic gas, originally at 1.00 atm and 10 ∘C, expands adiabatically to 1.75 times its initial volume. What are the final temperatures for the gas?
2) An ideal monatomic gas, consisting of 2.8 mol of volume 8.3×10−2 m3 , expands adiabatically. The initial and final temperatures are 95 ∘C and -81 ∘C. What is the final volume of the gas?
P_1*V_1 = P_2*V_2
PV = nRT
PV^γ = constant
TV^(γ-1) = constant
The Attempt at a Solution
Attempt at #1[/B]: I know we needed final pressure for this; I had calculated it and was told it was correct. Though the answer was rounded, I kept my final pressure unaltered, since the calculator I am using allows me to assign single letter variables to numerical constants. The final pressure I got was 1 * (1/1.75)^1.4 =~ .457 when rounded.
I calculated the true initial volume via the constants given; I converted the pressure (1 atm) to 101325 Pascals, and the temperature from Celsius to Kelvin. I then solved for Volume, then I multiplied by 1.75 to get the final volume, which gave me approximately .0398, but I again did not round and assigned it to a letter. I used algebra to get T_f = P_f*V_f / n*R = about 221 when rounded (like the other values, I assigned it a letter for an exact number). Then I subtracted 273.15 from that number and got about -52 degrees Celsius; rounded to two sigfigs as requested by the problem. But that is still wrong; I do not know where my error is.
Attempt at #2: I felt this was simple, T_1*(V_1)^(1.4-1) = T_2*(V_2)^(1.4-1). Once again I set up my equation by changing Celsius to Kelvin, and we already had V_1, so I felt it was simple algebra.
I solved for V_2, which came out to be about .42 (4.2 * 10^-1) which I felt was reasonable given there was such a sharp decrease in temperature. Again, I was told I was wrong and I am not sure why.