A rigid tank (volume = V) containing an ideal gas is initially at T, and P. At time zero, an exit pipe (area = A) is opened and gas flows out of the tank at velocity v = K(P – Pam)2, where P is the pressure in the tank, Pam is the pressure of the atmosphere outside the tank, and K is a constant. The temperature of the gas in the tank is maintained at T, during the process. The pressure and the temperature of the gas exiting the tank are Pm and T1, respectively. Assume that, inside the tank, the pressure and specific volume do not vary with position. A. Derive a differential equation for the tank pressure P as a function of time t. B. Determine the time required for the tank pressure to reach P. atm

5. (a) There is 1000 kg water in a swimming pool. Consider the liquid water as an incompressible model at room temperature. If the temperature of the water body is increased by 3 degrees C (assuming this temperature change is uniform across the entire pool), determine: (i) the total internal energy change of the water, (ii) the total enthalpy change of the water. Use a constant heat capacity of water c = 4.211 kJ/kg. K. (b) In a big closed room, there is 1000 kg of air. Suppose the air is an ideal gas model at room temperature. The temperature of the room is increased by 3 degrees C heated by an electric heater. Suppose this temperature change is uniform across the entire room. (iii) Determine the total internal energy change of the air. (iv) Determine the total enthalpy change of the air. Use constant heat capacities of air c₂ = 0.718 kJ/kg . K and Cp = 1.005 kJ/kg.K.

Q. - ome kg of an ideal gas (R = 287 J um irreversible Process from Stelte - 0 [1 bar, 300 k] to State - [2 bar, 300k]. The entropy change (S2-S1) J kg-k