Astrophysics

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GRE Subject Test: Physics › Astrophysics

Questions 1 - 3

If the temperature of a blackbody doubles, what occurs to the wavelength of maximum emission?

It is halved.

It doubles.

It quadruples.

No change.

It is quartered.

Explanation

This is an application of Wein's Law that states the following:

$\lambda_{max}=\frac{0.0029Km}{T}$ , where $\lambda_{max}$ is the wavelength of maximum emission of the object (measured in ), and is the temperature in . Since the wavelength and the temperature are inversely proportional, if we double the temperature, we must cut the wavelength by the same proportion. Therefore, the temperature must be halved.

By what factor will the energy emitted each second off the surface of a blackbody change if the the temperature of the object is tripled?

$\frac{1}{3}$

Explanation

Stefan-Boltzmann's equation for a blackbody states:

$F=\sigma T^4$ , where is the energy emitted each second, $\sigma$ is the Stefan-Boltzmann constant, and is the temperature of the blackbody. Therefore, if we triple the temperature, the energy will increase by a factor of

Using the kinetic theory of gas, what is the fundamental property of a planet that dictates if it is able to retain an atmosphere?

Mass

Temperature

Energy

Number of moons

Magnetic field strength

Explanation

The kinetic theory of gas states:

$v_{rms}=\sqrt{\frac{3kT}{m}}$ . Whenever the velocity of the individual gas particles is larger than the escape speed of the planet,

$v_e=\sqrt{\frac{2GM}{r}}$ , the gas particles will leak into space and deplete the atmosphere. The physical property that determines this is the mass of the planet.

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