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SOLUTIONS TO EXERCISE 24
(a) The formula for pressure, with values plugged in for the Sun's mass and radius, comes out to P = 19 * (GM/R^2) * (M/R^2) = 19 * GM^2/R^4 = 19 * (6.67 * 10^(-11)) * (2.0 * 10^30 kg)^2 / (7.0 * 10^8 m)^4 = 2.1 * 10^16 N/m^2 Compared to Earth's atmospheric pressure of 1.01 * 10^5 N/m^2, this is (2.1 * 10^16) / (1.01 * 10^5) = 200 billion times greater. (b) If we treat the Sun as an ideal gas and use P = nkT, then use the values given for n and k, we get (2.1 * 10^16 N/m^2) = (1.0 * 10^32/m^3) * (1.38 * 10^(-23) J/K) * T and thus T = (2.1 * 10^16) / (1.38 * 10^9) = 1.5 * 10^7 K or 15 million degrees Kelvin. Some hot things on Earth include the Sahara Desert (about 330 K), a blast furnace (about 2000 K), light bulb filaments (about 2500 K), and our planet's molten core (about 4000-6000 K). None of these are even one-thousandth the temperature at the Sun's core. However, human beings are able to produce Sun-like temperatures artificially: the temperature of a nuclear explosion can reach 10 million degrees K. |