P2.10. A block of copper weighing 0.2 kg with an initial temperature of 400 K is dropped into 4 kg of water initially at 300 K contained in a perfectly insulated tank. The tank is also made of copper and weighs 0.5 kg. Solve for the change in internal energy of both the water and the block given CV = 4.184 J/g-K for water and 0.380 J/g-K for copper. (ANS. 7480 J, 7570 J) P2.11. In the preceding problem, suppose that the copper block is dropped into the water from a height of 50 m. Assuming no loss of water from the tank, what is the change in internal energy of the block? (ANS. 7570 J) P2.12. In the following take CV = 5 and CP = 7 cal/mol-K for nitrogen gas: a. Five moles of nitrogen at 100C is contained in a rigid vessel. How much heat must be added to the system to raise its temperature to 300C if the vessel has a negligible heat capacity? (ANS. 5000 cal) If the vessel weighs 80 g and has a heat capacity of 0.125 cal/g-K, how much heat is required? (ANS. 7000 cal) b. Five moles of nitrogen at 300C is contained in a piston/cylinder arrangement. How much heat must be extracted from this system, which is kept at constant pressure, to cool it to 100C if the heat capacity of the piston and cylinder is neglected? (ANS. 7000 cal) P2.13. A rigid cylinder of gaseous hydrogen is heated from 300 K and 1 bar to 400 K. How much heat is added to the gas? (ANS. 2080 J/mole) P2.14. Saturated steam at 660F is adiabatically throttled through a valve to atmospheric pressure in a steady-state flow process. Estimate the outlet quality of the steam. (ANS. q = 0.96) P2.15. Refer to Example 2.10 about transformation of kinetic energy to enthalpy. Instead of water, suppose N2 at 1 bar and 298 K was flowing in the pipe. How would that change the answers? In particular, how would the temperature rise change? (ANS. max ~0.001K) P2.16. Steam at 150 bars and 600C passes through process equipment and emerges at 100 bars and 700C. There is no flow of work into or out of the equipment, but heat is transferred. a. Using the steam tables, compute the flow of heat into the process equipment per kg of steam. (ANS. 288 kJ/kg) b. Compute the value of enthalpy at the inlet conditions, Hin, relative to an ideal gas at the same temperature, Hig. Consider steam at 1 bar and 600C as an ideal gas. Express your answer as (Hin Hig)/RTin. (ANS. 0.305) P2.17. A 700 kg piston is initially held in place by a removable latch above a vertical cylinder. The cylinder has an area of 0.1 m2; the volume of the gas within the cylinder initially is 0.1 m3 at a pressure of 10 bar. The working fluid may be assumed to obey the ideal gas equation of state. The cylinder has a total volume of 0.25 m3, and the top end is open to the surrounding atmosphere at 1 bar. a. Assume that the frictionless piston rises in the cylinder when the latches are removed and the gas within the cylinder is always kept at the same temperature. This may seem like an odd assumption, but it provides an approximate result that is relatively easy to obtain. What will be the velocity of the piston as it leaves the cylinder? (ANS. 13.8 m/s) b. What will be the maximum height to which the piston will rise? (ANS. 9.6 m) c. What is the pressure behind the piston just before it leaves the cylinder? (ANS. 4 bar) d. Now suppose the cylinder was increased in length such that its new total volume is 0.588 m3. What is the new height reached by the piston? (ANS. ~13 m) e. What is the maximum height we could make the piston reach by making the cylinder longer? (ANS. ~13 m) P2.18. A tennis ball machine fires tennis balls at 40 mph. The cylinder of the machine is 1 m long; the installed compressor can reach about 50 psig in a reasonable amount of time. The tennis ball is about 3 inches in diameter and weighs about 0.125 lbm. Estimate the initial volume required in the pressurized firing chamber. [Hint: Note the tennis ball machine fires horizontally and the tennis ball can be treated as a frictionless piston. Dont be surprised if an iterative solution is necessary and ln (V2/V1) = ln(1 + V/V1)]. (ANS. 390 cm3) P2.19. A 700 kg piston is initially held in place by a removable latch inside a horizontal cylinder. The totally frictionless cylinder (assume no viscous dissipation from the gas also) has an area of 0.1 m2; the volume of the gas on the left of the piston is initially 0.1 m3 at a pressure of 8 bars. The pressure on the right of the piston is initially 1 bar, and the total volume is 0.25 m3. The working fluid may be assumed to follow the ideal gas equation of state. What would be the highest pressure reached on the right side of the piston and what would be the position of the piston at that pressure? (a) Assume isothermal; (b) What is the kinetic energy of the piston when the pressures are equal?16 (partial ANS. 1.6 bars)