Thermodynamics

7–182 The explosion of a hot water tank in a school inSpencer, Oklahoma, in 1982 killed 7 people while injuring 33others. Although the number of such explosions hasdecreased dramatically since the development of the ASMEPressure Vessel Code, which requires the tanks to be designedto withstand four times the normal operating pressures, theystill occur as a result of the failure of the pressure reliefvalves and thermostats. When a tank filled with a highpressureand high-temperature liquid ruptures, the suddendrop of the pressure of the liquid to the atmospheric levelcauses part of the liquid to flash into vapor, and thus to experiencea huge rise in its volume. The resulting pressure wavethat propagates rapidly can cause considerable damage.Considering that the pressurized liquid in the tank eventuallyreaches equilibrium with its surroundings shortly afterthe explosion, the work that a pressurized liquid would do ifallowed to expand reversibly and adiabatically to the pressureof the surroundings can be viewed as the explosive energy ofthe pressurized liquid. Because of the very short time periodof the explosion and the apparent calm afterward, the explosionprocess can be considered to be adiabatic with nochanges in kinetic and potential energies and no mixing withthe air.Consider a 80-L hot-water tank that has a working pressureof 0.5 MPa. As a result of some malfunction, the pressure inthe tank rises to 2 MPa, at which point the tank explodes.Taking the atmospheric pressure to be 100 kPa and assumingthe liquid in the tank to be saturated at the time of explosion,determine the total explosion energy of the tank in terms ofthe TNT equivalence. (The explosion energy of TNT is about3250 kJ/kg, and 5 kg of TNT can cause total destruction ofunreinforced structures within about a 7-m radius.) Answer:1.972 kg TNTHot watertank80 L2 MPaREV.HEHigh-temperature reservoir at T HQ HQ LW net,revIRREV.HELow-temperature reservoir at T LFIGURE P7–184Chapter 7 | 4177–185 The inner and outer surfaces of a 2-m 2-m windowglass in winter are 10°C and 3°C, respectively. If therate of heat loss through the window is 3.2 kJ/s, determinethe amount of heat loss, in kilojoules, through the glass overa period of 5 h. Also, determine the rate of entropy generationduring this process within the glass.7–186 Two rigid tanks are connected by a valve. Tank A isinsulated and contains 0.2 m 3 of steam at 400 kPa and 80percent quality. Tank B is uninsulated and contains 3 kg ofsteam at 200 kPa and 250°C. The valve is now opened, andsteam flows from tank A to tank B until the pressure in tankA drops to 300 kPa. During this process 600 kJ of heat istransferred from tank B to the surroundings at 0°C. Assumingthe steam remaining inside tank A to have undergone areversible adiabatic process, determine (a) the final temperaturein each tank and (b) the entropy generated during thisprocess. Answers: (a) 133.5°C, 113.2°C; (b) 0.916 kJ/KQ HQ L, irrev600 kJW net,irrevFIGURE P7–1827–183 Using the arguments in the Prob. 7–182, determinethe total explosion energy of a 0.35-L canned drink thatexplodes at a pressure of 1.2 MPa. To how many kg of TNTis this explosion energy equivalent?7–184 Demonstrate the validity of the Clausius inequalityusing a reversible and an irreversible heat engine operatingbetween the same two thermal energy reservoirs at constanttemperatures of T L and T H .A0.2 m 3steam400 kPax = 0.8FIGURE P7–186B3 kgsteam200 kPa250°C7–187 Heat is transferred steadily to boiling water in thepan through its flat bottom at a rate of 500 W. If the temperaturesof the inner and outer surfaces of the bottom of the tank