Answer: 296.17 K
Explanation:
This question is a specific heat capacity question. Heat capacity is the proportionality constant which shows the relationship between the change in temperature and the heat,q.
It can represented mathematically by;
C= q/∆T------------------------------------***
STEP ONE:
Note that, ∆U= q---------------------------------------------------------------------------1).
DU= nCv∆T------------------------------(2).
PV= n×R×T (ideal gas equation)------------------------------------------------------(3).
Recall that ∆U= q; ∆U= nCv∆T. Substitute equation (3) into equation (2).
Hence, ∆U= (PV/RT) Cv∆T------------------------------------------------------------(4).
∆U= (PV/RT) Cv(T(f)- Ti). Where T(f)= final temperature and Ti= initial temperature.
Therefore, T(f )= Ti + RTiq/ PVCv -----------------------------------------------(5).
Slotting in the parameters given into equation (5).
T(f)= [(23+273.15)+ 8.314×2.66×10^4 × (23+273.15) ] ÷ 35×425×1.013×10^5× 20.8.
T(f)= 296.17 K.
