determine the final state for the gas in an inflated balloon.

We wish to determine the final state for the gas in an inflated balloon. Initially, the balloon has a volume of V ⁱ at rest. The volume of the balloon is related to the internal pressure by V = a·P + b, where a and b are constants. The balloon is to be inflated by air from our lungs at P_lung and T_lung which are known and assumed to remain constant during inflation. Heat transfer through the walls of the balloon can be ignored. The system is defined to be the gas inside the balloon at any time. Starting with the general energy balance, simplify to write the balance in terms of {C_P, C_V, T_lung, P_lung, T_i, T_f, T_R, P_R } and either {Vⁱ, V^f } or { Pi,P^f }. This will demonstrate that measurement of V^f or P^f is sufficient to determine T^f. Assume air is an ideal gas.