A 4.40 mol sample of an ideal diatomic gas expands adiabatically from a volume of 0.121 m3 to 0.60 m3. initially the pressure was 1.00 atm. (assume no molecular vibration.) (a) determine the initial and final temperatures.

First, we have to get Pf from this formula:

Pf = Pi * (Vi/Vf) ^γ

when Pi = 1 atm = 1 * 1.01325 x 10^5 Pa

Vi = 0.121 m^3

Vf = 0.6 m^3

and gamma γ = 1.4

by substitution:

∴ Pf = 1 atm * (0.121 / 0.6) ^1.4

= 0.11 atm = 11145.75 Pa

a) to get initial T:

when Pivi = nRTi

by substitution

(1.01325 x 10^5) * 0.121 = 4.4 * 8.31 * Ti

∴Ti = 335 K

b) to get Tf:

PfVf = nRTf

by substitution:

11145.75 * 0.6 = 4.4 * 8.31 * Tf

∴ Tf = 183 K