Question

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?

Answer 1

Answer:

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

$V = \frac{(1)(0.257)(298)}{300}$

V = 0.25 $m^{3}$

Mole number of oxygen is

$N o_{2} = \frac{m}{M}$

$N o_{2} = \frac{1}{32}$

$N o_{2} =$ 0.03125 k mol

Given data for nitrogen

Volume of Nitrogen = 2 $m^{3}$

Temperature = 50  °c= 323 K

Pressure = 500 K pa

Mass of nitrogen

m = $\frac{(500)(2)}{(0.297)(323)}$

m = 10.43 kg

Now mole number of nitrogen

$N n_{2} = \frac{10.43}{28}$

$N n_{2} =$ 0.372 k mol

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

N = $N o_{2} + N n_{2}$

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 $m^{3}$

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