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A container contains 2 moles of a gas at a pressure of 8 atm and a temperature of 300 K. Calculate the volume of the gas in each of the following thermodynamic ensembles: microcanonical, canonical, and grand canonical ensembles.

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In all three ensembles, we can use the Ideal Gas Law to calculate the volume of the gas. The Ideal Gas Law is given by:PV = nRTwhere P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.Given the problem, we have:P = 8 atmn = 2 molesR = 0.0821 L atm /  mol K   ideal gas constant in appropriate units T = 300 KNow, we can solve for the volume V:V = nRT / PV =  2 moles  *  0.0821 L atm /  mol K   *  300 K  /  8 atm V = 6.156 LSo, the volume of the gas in each of the microcanonical, canonical, and grand canonical ensembles is 6.156 L. Note that the ensemble type does not affect the volume calculation in this case, as we are using the Ideal Gas Law, which is applicable to all three ensembles.

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