Compared how much impulse is potentially created by heating up a gas as compared to the impulse created by the laser for the same amount of energy. Find that the gas can get a million times more impulse per energy increase. If the heat source was a heater that only heats things up by radiating photons, how did the gas end up with a million times more impulse change than the photons from the heater had originally? 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.