Answer:
Final temperature = 152.57K,
Pressure = 0.6907 bar.
dT/dt = - 1,151 K/s.
Explanation:
The first thing to do here is to write out the equation for mass balance as given below:
dN/dt = N -------------------------------------------------------------------------------------------(1).
N = P/T, then, substitute the values given in the question into:
d[p/T]/ dt = [- 4.5/28 × 8.314]/0.15 = - 8.9 × 10⁻⁵ bar/K.s.
Thus, there is the need to integrate, Integrate [p/T]f = 10/320 - 8.9 × 10⁻⁵ bar/K.s. ------------------------------------(2).
NB; fT = final temperature, fP = final pressure and iT = initial temperature.
Also, [ fT]³⁰/₈.₃₁₄/ [fP] = [iT]³⁰/₈.₃₁₄/ Pi] = [ 320]³⁰/₈.₃₁₄/ 10.
Therefore, [fT]³⁰/₈.₃₁₄ = 109.52 × 10⁶.
Final temperature= [fP]³⁰/₈.₃₁₄ × 169.05.
Note that fP/ [fP]³⁰/₈.₃₁₄ × 169.05 = 10/320 - 8.9 × 10⁻⁵.
Therefore, [fP]¹ ⁻ ³⁰/₈.₃₁₄ = 0.7651.
Hence, Final temperature = 152.57K,
Pressure = 0.6907 bar
dT/ dt = N[RT]² / Cv . PV.
R = 30 - 8.314 = 21.86 J/mol K.
Then, the rate of change of the gas temperature at this time = dT/dt = - 1,151 K/s.
