Find the final volume V in an adiabatic process?

Question

A flexible balloon contains 0.370 mol of hydrogen sulfide gas H2S. Initially the balloon of H2S has a volume of 6750 cm^3 and a temperature of 26.0 C. The H2S first expands isobarically until the volume doubles. Then it expands adiabatically until the temperature returns to its initial value. Assume that the H2S may be treated as an ideal gas with C_p = 34.60 J/mol*K and gamma = 4/3.

The question is: What is the final volume V (in m^3)?

So far I found Q=W=3830 J, DeltaU= 0 J, and I also know that T*V^(gamma - 1) is a constant therefore T_1*V_1^(gamma - 1) = T_2*V_2^(gamma - 1) so I isolate V2 and get

V_2^(1/3)=[T_1 * V_1^(1/3)] / T_2

T_1 = initial Temp

T_2 = final temp

V_1 = initial volume

V_2 = final volume

so from the problem I gathered that:

V_1 = 135m^3

V_2 = ?

T_1 = ?

T_2 = 299 K

Is this correct? I need help finding T_1 in order to find V_2 (final V) and I've been stuck on this problem since last night!!! Any ideas will be helpful!

Thanks!!

Answer 1

The initial expansion is isobaric, so pressure remains the same.

P0 = n*R*T0/V0, where

P0 = initial pressure

n = no of moles of H2S. (0.370)

V0 = initial volume (6750 cm³)

T0 = initial temperature.  (299 ºK)

after expansion

P1*V1 = n*R*T1;

T1 = P0*2*V0/(n*R)

T1 = n*R*T0/V0 * 2*V0 / n*R

T1 = T0/V0 * 2*V0 = 2*T0

EDIT:  In your work you show V_1 = 135 m³; but 2*6750 cm³ = 0.0135 m³.  Could that be the problem?