An insulated tank that contains 1 kh of O2 and 15C and 300 kPa is connected to a 2m uninsulated tank that contains N2 at 50C and 500 kPa. The valve connecting the two tanks is opened, and the two gases form a homogenous mixture at 25C. Determine the final pressure in the tank, the heat transfer?

The final pressure of the mixture = 444.4 k pa

Explanation:

Given data for oxygen

Mass of oxygen = 1 kg

Temperature = 15 °c= 298 K

Pressure P = 300 K pa

Volume of the oxygen

V = 0.25

Mole number of oxygen is

0.03125 k mol

Given data for nitrogen

Volume of Nitrogen = 2

Temperature = 50  °c= 323 K

Pressure = 500 K pa

Mass of nitrogen

m =

m = 10.43 kg

Now mole number of nitrogen

0.372 k mol

Thus the mole number of mixture is the sum of mole no. of oxygen & mole no. of nitrogen.

N =

N = 0.03125 + 0.372

N = 0.4035 k mol

Therefore the final pressure of the mixture is given by the ideal gas equation

P V = N R T  ------- (1)

Where P = final pressure of the mixture

V = 0.25 + 2 = 2.25

N = total no. of moles in final mixture  = 0.4035 K mol

T = final temperature of the mixture = 298 K

Put all the values in  equation 1 , we get

P × 2.25 = 0.4035 × 8.314 × 298

P = 444.4 K pa

Therefore the final pressure of the mixture = 444.4 k pa

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