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A rigid vessel of $0\mathrm{.}06$ m$3$ volume contains an ideal gas, CV $=(5/2)$R$,$ at $500$ K and $1$ bar. $($a$)$ If heat in the amount of $15,000$ J is transferred to the gas, determine its entropy change. $($b$)$ If the vessel is fitted with a stirrer that is rotated by a shaft so that work in the amount of $15,000$ J is done on the gas, what is the entropy change of the gas if the process is adiabatic? What is $$Stotal$?$ What is the irreversible feature of the process?