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An insulated, isolated canister contains a monatomic ideal gas, described by the state parameters: U,P,V,N and T. A quantity of energy in the form of heat, Q, is suddenly added to this gas while keeping the volume and number of particles fixed. (vii) Derive an expression for the change in entropy of this gas after the system has reached equilibrium in terms of the state parameters of the initial state (U,P,V,N and T) plus the heat energy added, Q. [Mark: 15 percent] (viii) Show that this change in entropy is positive. [Mark: 5 percent]