# Homework Help: Pressure and volume

1. Sep 10, 2011

### TyErd

1. The problem statement, all variables and given/known data
I have attached the question. I have no clue with this one. Is there a specific equation that I have to use? How do I approach a problem like this??

2. Relevant equations
density = mass/volume
specific volume = volume/mass = 1/density
mass flow rate = density x volume flow rate
volume flow rate = cross sectional area x velocity
density of water = 1000kg/m^3
density of air = 1.22521kg/m^3 i think?
total volume = mass x specific volume

3. The attempt at a solution
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2. Sep 10, 2011

Write down the ideal gas equation PV=nRT for each container's initially while assuming unknowns.

3. Sep 10, 2011

Then we know that total no. of moles in system(container 1 + container 2) is constant.
Then write final gas equation PV=(n1+n2)RT.

Sufficient data is given to you.Molar mass of air may be required

4. Sep 10, 2011

### TyErd

okay so the ideal gas law eqs: 500 x 10^3 (1) = n x 287 x (25 +273.15)------container 1.
200 x 10^3 (V) = n x 287 x (35 +273.15)------------container 2.

how do i find Volume knowing that it weighs 5kg. Am i suppose to add the two above equations?? then make it equal to P (V1+V2)=(n1+n2) x 287 x (20 + 273.15) ???????

5. Sep 10, 2011

You know the volume of second tank using ideal gas equation for container-2.You have pressure temperature and number of moles(you need molar mass of air).

6. Sep 10, 2011

Using this you get V1+v2 in final equation.There you have total no. of moles, total volume and equilibrium temperature.Get equilibrium Pressure

7. Sep 10, 2011

### TyErd

I'm not sure i understand what you mean. Isn't the molar mass used to find R in the ideal gas law equation??? I used R as 287 is that right??? i dont get how to find n

8. Sep 10, 2011

molar mass of air is 28.97 and R is 8.31J/mol*K.
You are using wrong values of R.

9. Sep 10, 2011

In the ideal gas equation for first container you have temperature, pressure, and volume calculate no. of moles for container 1.

10. Sep 10, 2011

For second container you have mass of air 5kg=5000g.
no. of moles= 5000/28.97=172.59

11. Sep 10, 2011

### legendary_

Here is how to solve the problem:

Use finite states to have a picture of the problem easily.

State 1:
V_a1 = 1 m^3
T_a1 = 25 deg C + 273 = 323 K
P_a1 = 500 kPa
m_b1 = 5 kg
T_b1 = 35 deg C + 273 = 308 K
P_b1 = 200 kPa

State 2:
T_a2 = T_b2 = 20 deg C + 273 = 293 K (thermal equilibrium w/ surroundings)
V_b2 = ?
P_b2 = ?

where a is the first tank, and b is the second tank.

Solution:
1. Obtain unknowns of each tank for easy computations at the initial state or State 1.

1.1 Obtain the mass of the first tank using PV=mRT
m_a1=P_a1*V_a1 / (R*T_a1), where R is 286.9 J/(kgK)

1.2 Obtain the volume of the second tank
V_b1= m_b1 * R * T_b1 / P_b1

2. Analyze the transition from State 1 to State 2, taking note of the parameters in PV=mRT equation.

2.1 When the valve is opened, the volume of the 2 tanks will not obviously change. So the volume of the second tank V_b2 is equal to V_b1.

2.2 Since the valve is already opened, the contents of the 2 tanks are combined, that is: m_a1 + m_b1 = m_a2 = m_b2. Now, we can solve for the final pressure using PV = mRT:
P_b2 = m_b2 * R * T_b2 / V_b2

12. Sep 10, 2011

How come R is 286.9????It's 8.31 as i said earlier.
You will need molar mass of air.

13. Sep 10, 2011

### TyErd

8.31 im pretty sure is the universal gas constant. to find the gas constant of air it is universal gas constant divided by molar mass. R of air = universal gas constant (8.31) / molar mass of air(28.956) = 0.2869kPa = 286.9Pa

14. Sep 10, 2011

### TyErd

anyway my working out now is:
container 1: 500 x 10^3 (1) = m x 287 x (25 + 273.15) thus m = 5.84kg.
container 2: 200 x 10^3 (V) = 5 x 287 x (35 + 273.15) thus V = 2.21 m^3

so mass total is 5.84 + 5 = 10.84 kg

therefore P ( 2.21) = 10.84 x 287 x (20 + 273.15), which means P = 412616 Pa = 412.6kPa. Is that correct?

15. Sep 10, 2011

Then it's okay.However using universal gas constant seems more fundamental.

16. Sep 10, 2011

### TyErd

is my working out correct as well?

17. Sep 10, 2011

seems OK.Check for any calculation errors and if your answer matches with correct answer(if known) then fine.

18. Sep 11, 2011

### TyErd

to find the final equilibrium pressure, what volume do i have to use? the volume of the first/second or both added together?

19. Sep 11, 2011