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Jedi_Sawyer

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Calculation for those that don't take my word for it,

Let us use nitrogen gas and the ideal gas law, PV = nRT

R is the gas constant 8.314 J/(mol K),

We will be using 28 grams for the molecular weight of a mol of N2 molecules.

Volume of 1 m3

4 Mols of Nitrogen

Temperature of 200o K

P V= nRT = (6651.2 Kg )/ (m s2) x 1.0 m3 = 4 x 8.314 J x 200 = 6651.2 J

Now we want to add enough energy to bring the temperature up to 800oK

Volume of 1 m3

4 Mols of Nitrogen

Temperature of 800o K

P V= nRT = (6651.2 Kg )/ (m s2) x 1.0 m3 = 4 x 8.314 J x 800 = 26604.8 J

So in order to raise the temperature of our gas to 800 we added 19953.6 J of energy, and now we want to know how much the impulse was potentially increased by adding that energy.

Knowing that we have 4 mols of N2 nitrogen, the mass is 4x28grams or

.112 Kg and using ½ Mv2 we allow it to equal 26604.8 J we get

½ x .112 Kg x v2 = 26604.8 J v = 974.8 m/s so Mv = 109.2 Kg m/s

We have to subtract the impulse we had that we originally had at 6651.2 J

½ x .112 Kg x v2 = 6651.2 J v = 344.6 m/s so Mv = 38.6 Kg m/s

Adding 19953.6 J to this gas, we gained 109.2 - 38.6 = 70.6 Kg m/s Impulse. At least potentially.

Now we are going to calculate the Impulse created by lasers and of two different types for 19953.6 J output from these lasers.

Speed of light 2.99 e 8 meters

Ruby Laser 694.3 nm = 1.35 x 10^15 Hz

Helium – Silver Laser 224.3 nm = 4.17 x 10^15 Hz

Energy per photon = hf or hc/λ

= 2.86 e-13 u J Ruby laser photon

= 8.86 e-13 µ J Helium-Silver Laser photon

For our example in order to have 19953.6 J in photons we need:

19953.6 J / 2.86 e-19 J = 6.96 e 22 Ruby photons

19953.6 J / 8.86 e-19 J = 2.25 e 22 Helium-Silver Laser photon

To get the momentum for a photon divide the photon's energy by the speed of light

Momentum per photon = 9.57 e -28 kg x m/sec for Ruby laser photon

Momentum per photon = 2.96 e -27 kg x m/sec Helium-Silver photon

For 19953.6 Joules turned into photons for ideal directional momentum = 6.69 e-5 Kg x m/sec for a Ruby laser

= 6.69 e-5 Kg x m/ sec for Helium-Silver laser, so the result is independent of frequency.

For an added 19953.6 Joules we got an impulse increase of 70.6 Kg m/s by heating our gas and only 6.69 e-5 Kg m/s by using laser light.

This result indicates that gas rockets are a million times more efficient at turning energy into impulse.