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.

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Chemistry

Logan

7 June, 10:41

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.

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Lindsay Warren · Answer 1

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