Answer:
the final temperature is 77.1 °C
Explanation:
Given the data in the question;
Initial temperature; T₁ = 27°C = ( 27 + 273)K = 300 K
Initial absolute pressure P₁ = 300 kPa = ( 300 + 101.325 )kPa = 401.325 kPa
Final absolute pressure P₂ = 367 kPa = ( 367 + 101.325 )kPa = 468.325 kPa
Now, to calculate the final temperature, we use the ideal gas equation;
P₁V/T₁ = P₂V/T₂
but it is mentioned that the rigid tank is closed,
so the volume is the same both before and after.
Change in volume = 0
hence;
P₁/T₁ = P₂/T₂
we substitute
401.325 kPa / 300 K = 468.325 kPa / T₂
T₂ × 401.325 kPa = 300 K × 468.325 kPa
T₂ = [ 300 K × 468.325 kPa ] / 401.325 kPa
T₂ = 140497.5 K / 401.325
T₂ = 350.08 K
T₂ = ( 350.08 - 273 ) °C
T₂ = 77.1 °C
Therefore, the final temperature is 77.1 °C
