# Formula for Work to create a vacuum.

by Arnak
Tags: formula, vacuum, work
 P: 6 Hi, Can someone give me some guidance on how to calculate the work or energy required to create a vacuum. For example, I would like to create a 2.5psi vacuum in a tube of a specific length and diameter using a pneumatic cylinder to remove the air. How would I go about calculating the energy required to do that please? From that answer I want to calculate the power of an electric motor required to perform that task. Thanks, Arnak
P: 112
 Quote by Arnak Hi, Can someone give me some guidance on how to calculate the work or energy required to create a vacuum. For example, I would like to create a 2.5psi vacuum in a tube of a specific length and diameter using a pneumatic cylinder to remove the air. How would I go about calculating the energy required to do that please? From that answer I want to calculate the power of an electric motor required to perform that task. Thanks, Arnak
The work to create difference in pressure is

W = dP*V*t

dP is the pressure difference
V is the volume of the air container
t is the time for what you have achieved the pressure difference

Here the heat transfer is not taken in account.
P: 101
 Quote by Malverin The work to create difference in pressure is W = dP*V*t dP is the pressure difference V is the volume of the air container t is the time for what you have achieved the pressure difference Here the heat transfer is not taken in account.
Why do you need time here ?

P: 6

## Formula for Work to create a vacuum.

Hi,

Thanks for that formula.9-))

What units would the work be in please?

Am I right in saying then that with a cylinder of 200 x 50mm V= 10000 mm3

Pressure difference = 2.5psi

So 10000 x 2.5 = 25000 units?

Arnak
P: 112
 Quote by regor60 Why do you need time here ?
I have confused work with power here.

The power is

Power = dP*V / t

so work is only

W = dP*V

My mistake. Sorry
P: 112
 Quote by Arnak Hi, Thanks for that formula.9-)) What units would the work be in please? Am I right in saying then that with a cylinder of 200 x 50mm V= 10000 mm3 Pressure difference = 2.5psi So 10000 x 2.5 = 25000 units? Arnak
The formula has to be

W = dP*V

t has no place there. My mistake

in SI system, units are

W => Joules
dP => Pascals
V => m3
P: 705
 Quote by Malverin The work to create difference in pressure is W = dP*V*t dP is the pressure difference V is the volume of the air container t is the time for what you have achieved the pressure difference
Not quite.

Consider the ideal case of a cylinder and a piston. You have a volume V of an ideal gas at ambient pressure Pamb and you want to exhaust enough gas to end up with the same volume V at reduced pressure Pnew.

That means that you need to push the piston to exhaust a volume V * (1 - Pnew/Pamb) of gas at ambient pressure. Pushing against atmospheric pressure takes work equal to Pamb * V * (1 - Pnew/Pamb) = V * (Pamb - Pnew)

But this leaves you with a volume V * Pnew/Pamb of gas at ambient pressure with a total volume V available to expand into. That represents work that can be reclaimed. The formula for the work gained with the isothermal expansion of an ideal gas is Vinitial * Pinitial * ln(Pinitial/pfinal). The formula also works if you swap "initial" with "final" and negate the sign.

Putting that together gives you a required work of:

W = V * ( Pamb - Pnew ) + V * Pnew * ln(Pnew/Pamb)

As long as Pnew is lower than Pamb, the second term will be negative, so it subtracts from the work required.

If you are using a coherent system of units such as SI with volume in cubic meters, pressure in Pascals and work in Joules then the formula will work as is. If you are using pounds per square inch and cubic millimeters then some unit conversion factors will be required.
 P: 6 Hi Jbriggs, Thanks for the input.8-)) So by my calculations :- W = 0.00001*(101325 - 84088) + 0.00001 * 84088 * ln(84088/101325) W = 0.87020288682 Joules. Please excuse my lack of knowledge of algebra but is the component ln the designation for the result of (Pnew/Pamb)? I have converted the units to Pascals and M3. V= 0.00001 m3, Pamb = air pressure 101325 Pascals, Reduction of 2.5psi in Pascals =17237 So Pamb(101325) - Reduction of 17237 = Pnew = 84088 Have I got that right so far please? Can you also advise me where I can find a link to these equations so I can attempt to learn more? Martin
P: 705
 Quote by Arnak So by my calculations :- W = 0.00001*(101325 - 84088) + 0.00001 * 84088 * ln(84088/101325) W = 0.87020288682 Joules. Please excuse my lack of knowledge of algebra but is the component ln the designation for the result of (Pnew/Pamb)?
"ln" is natural logarithm. The natural log of 84088/101325 is approximately -0.19

 I have converted the units to Pascals and M3. V= 0.00001 m3, Pamb = air pressure 101325 Pascals, Reduction of 2.5psi in Pascals =17237 So Pamb(101325) - Reduction of 17237 = Pnew = 84088 Have I got that right so far please?
Looks good.