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One mole of an ideal, monatomic gas is allowed to expand from a volume of 6.0 L to a volume of 8.5 L.

For a reversible, adiabatic expansion, the following relationship follows from the first law of thermodynamics:

$${C}_{v}dT=-PdV$$

...where ${C}_{v}$ is the constant volume specific heat of the gas, $dT$ is the temperature differential, $p$ is the pressure of the gas, and $dV$ is the volume differential.

If the initial temperature of the gas is 350 K, what is the final temperature of the gas?

Note:

• ${C}_{v}=\cfrac{3}{2}R$
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