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Problem 20.7: Coefficient of expansion of an ideal gas
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When heated, materials expand in all three dimensions (position is given in meters). The equation for the volume expansion is as follows:
ΔV = Vo β ΔT,
where the change in volume (ΔV) is equal to the initial volume (Vo) multiplied by the coefficient of volume expansion, β, and by the temperature increase. Note that this equation is similar to the equation for linear expansion (see Exploration 19.2), and that for solids the coefficient of expansion, β, is approximately equal to 3α. Restart. For a gas we need to be careful because a gas can expand even without a change in temperature (if the pressure decreases).
- Assuming constant pressure, find the volume expansion coefficient of the gas at this initial temperature (100 K).
- Assuming an ideal gas, use PV = nRT to find (i.e., derive an expression for) the volume expansion coefficient and see that it varies with temperature (is not a constant).
- Pick a new initial temperature, use the animation, and verify that the results match the expression you derived.
Problem authored by Anne J. Cox.