Need help for undergrad chemistry problem (entropy calculation)

[Aschematic]

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0.1 moles of an ideal gas with Cv = 3R/2, initially confined to a container of volume 3 litre and at a temperature 6 C, expand (or are compressed) against a constant external pressure of 0.8 atm until the final pressure of the gas is equal to the external pressure and the final temperature of the gas is equal to the temperature of the surroundings. During this process the system does 4,354 J of work on the surroundings. Calculate the change in entropy, Delta S, of the gas (in J / K).


I first calculated P₁ by equating it to nRT₁/V₁.

Then I calculated V₂ by using w = -P_ext (V_f-V_i)

Then I calculated T₂ by using T₂ = P₂V₂/nR

Then I used the formula

Delta S = n C_v ln(T₂/T₁) + nR ln (V₂/V₁)
and plugged in the numbers to get 15.848



However, the correct answer is 6.2, which is just the latter portion of the Delta S equation "nR ln (V₂/V₁)".

I am wondering why you discard the former part of the Delta S equation "n C_v ln(T₂/T₁)"... Does that mean the two temperatures are somehow equal?

Please enlighten me as to what I did wrong. thank you!!

 

[hausee]

nevermind, too deep