Question

Methane initially at 50 kPa, 40◦C, is held in an insulated tank having a volume of 1.1 m3. An electric heating element within the tank adds heat at a constant rate of 500 J/s. Methane is bled from the tank to hold the pressure constant. Assuming that conditions are uniform throughout the tank at any instant, determine the time required for the methane to reach a temperature of 270◦C.

Answer 1

Initial pressure of methane = 50000 Pa

Initial temperature of methane = 400C

Volume of insulated tank = 1.1 m3

Initial amount of methane in the tank , nmethane
As we know that volume of tank is constant
P1 / T1 = P2 / T2
= 50000 / 313.15 = P2 / 543.15
= P2 = 86.72 (KPa)
Now
But to maintain initial presssure of 50 kPa, some gas has been bled from the tank, due to which amount of methane left in the tank is given by
Now doing heat balance we get
= 500 x t = 12.18 x 16 / 100 x x 3.074 x 1000 x (270 - 40)
= t = 275.568 (seconds).