A gas container is thermally isolated except for a small hole that insures that the pressure inside the container is equal to the atmospheric pressure p₀. Initially, the container holds N_i moles of gas at a temperature T_i. The molar specific heat of the gas at constant pressure is c_p. The gas is heated up to a temperature T_f by a resistive coil in the cylinder. As the gas temperature rises, some of the gas is released through the small hole. Assume that for the gas remaining in the cylinder the process is reversible and neglect the specific heat of the heater. Determine:

a) The volume V₀ of the container.

b) The number of moles ΔN leaving the container in this process.

c) The heat transfer Q_if to accomplish this process. Numerical Application:

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Po= 105 Pa, No = 10 moles, To = 273 K, cp = 29.1 J K-¹ mol-¹, T = 293 K.