Suppose a number of photons with spectrum corresponding to black body spectrum at 293 K with total energy corresponding to 1 kg put in a box with ideal mirror walls with volume of 1/1000 of a cubic meter (1 liter). What pressure this photonic gas will manifest on the walls of the box?
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Photons are radiation so their equation of state is $$ p = \frac{\rho}{3} $$ where $\rho$ is the energy density. So we have $$ p = \frac{mc^2}{3V} = \frac{1\times 9\times 10^{16}\,\,{\rm J}}{0.003\,{\rm m}^3} = 3 \times 10^{19}\,\,{\rm Pa}$$ It's a huge pressure. Not a surprising fact because the actual mass of photons we can produce is negligible. One kilogram worth of photons could be obtained by detonating a reasonable number of H-bombs: the mass would be taken from the difference between the helium and hydrogen nuclear masses. Note that in this parameterization, the result doesn't depend on the frequency/wavelength/temperature of the photons. |
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