Derive the seven general property equation of the following thermodynamics processes: a. ISOMETRIC PROCESS - Any Process relation - Work Non-flow - Internal Energy - Heat Transferred - Enthalphy - Entropy - Work Steady flow refer with the picture. Show all the detailed explanation
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- The Antoine Equation can be used to estimate vapor pressure at various temperatures for different substances using sets of empirically-derived constants. The equation can be written as: Where for water A = 8.07131, B = 1730.63, C = 233.426, T = temperature [°C], and P = vapor pressure [mmHg]. Note that with these constants the temperature and pressure must be provided in °C and mmHg, respectively. Using the Antoine Equation and the provided constants, what atmospheric pressure (provided in terms of % of standard atmospheric pressure) will permit water to boil at 75 °C?The ideal gas law relates the pressure P, volume V, absolute temperature T (Kelvin), and amount of gas n. The law is P = mAT where R is the gas constant. An engineer must design a large natural gas storage tank to be expandable to maintain the pressure constant at 2.2 atmospheres. In December when the temperature is -15°C, the volume of gas in the tank is 28,500 ft°. What will the volume of the same quantity of gas be in July when the temperature is 31°C? (Hint: Use the fact that n, R, and P are constant in this problem. Note also that Kelvin = °C+273.2)Completely solve and box the final answers. Write legibly 4. A single stage air compressor handles 30 cubic meter per minute of atmospheric pressure, 30°C air and delivers it to a receiver at 3.0 mpa. Its volumetric efficiency is 83.0%, compression efficiency of 83.0% and mechanical efficiency of 80.30%. If it rotates at 300 rpm, what power in kW is required to drive it?
- A certain ideal gas (unknown) inside a close piston-cylinder assembly undergoes a set of processesthat composed of Isothermal expansion from State point 1 to state point 2, Isometric heat rejectionfrom state point 2 to state point 3, and Isentropic compression from state point 3 back to the initialcondition. If the maximum pressure is 3000kPa and maximum and minimum volume is 200cm3and50cm3, analyze the problem and perform the following:a. Draw and label the graph of this set of processes in the P-V and T-S diagram showing the statepoint numbers and energy directions.b. From the known ideal gases as shown in Table 1.0, select the best suited ideal gas to attain theprocesses stated if the lowest pressure is limited to 629.8kPa. Assume a constant specific heat.c. For the selected ideal gas from b, compute the work of compression (kJ/kg), work of expansion(kJ/kg), and heat rejected (kJ/kgA certain ideal gas (unknown) inside a close piston-cylinder assembly undergoes a set of processesthat composed of Isothermal expansion from State point 1 to state point 2, Isometric heat rejectionfrom state point 2 to state point 3, and Isentropic compression from state point 3 back to the initialcondition. If the maximum pressure is 3000kPa and maximum and minimum volume is 200cm3and50cm3, analyze the problem and perform the following: a. Draw and label the graph of this set of processes in the P-V and T-S diagram showing the statepoint numbers and energy directions. b. From the known ideal gases as shown in Table 1.0, select the best suited ideal gas to attain theprocesses stated if the lowest pressure is limited to 629.8kPa. Assume a constant specific heat. c. For the selected ideal gas from b, compute the work of compression (kJ/kg), work of expansion(kJ/kg), and heat rejected (kJ/kg)Suppose four 30-g ice cubes are added to a glass containing 200 cm3 of orange juice at 20,0°C.You may assume that the orange juice has a density and specific heat capacity the same as water namely: Density = 1,0 g∙cm–3 and specific heat = 4,184 J/gK The heat of fusion (of water) is 333 J/g.Your task is twofold. You must determine:a) Whether or not all the ice will melt; andb) If your finding is that some ice will be left in the juice, you must calculate what mass of ice will be present the moment when thermal equilibrium is reached.
- Write the simplified ENERGY BALANCE equation for each process based on the givenconditions. Start from the general energy balance form, and arrive at the correct balance byexplaining any addition, deduction, or change in the equation.Use the following as subscripts in your answer: 1 = initial system state; 2 = final system state; i = inletstate, e = exit state.a. A rigid tank transferring heat to its surroundings. b. The seal of an insulated system with a high energy substance is broken, causing the contents tobe evacuated until only 20% of the initial internal energy remained. No heat transfer was detectedin the system’s boundaries. c. Consider a hydroelectric power plant operating in steady conditions, wherein the system consistsof two water reservoirs with a height difference Δz, with a Francis water turbine placed betweenthe stream connecting both.Solve the following problems and sketch the schematic diagram describing the system. Show pertinent and complete solutions. A certain ideal gas X has molecular weight of 10 g/mol and specific heat ratio of 2. Initially, X has pressure of 200kPa and volume of 2m3. The pressure was doubled during heat transfer. Find the heat transfer if it underwent a process described by; a. n=infinity b. n=Cp/Cv c. n=3A hot water leak in one of the faucets of your apartment can be very wasteful. A continuous leak of one quart per hour (a “slow” leak) at 155◦F causes a loss of 1.75 million Btu per year. Suppose your water is heated with electricity. Solve, a. How many pounds of coal delivered to your electric utility does this leak equate to if one pound of coal contains 12,000 Btu and the boiler combustion process and water distribution system have an overall efficiency of 30%? b). If a pound of coal produces 1.83 pounds of CO2 during the combustion process, how much extra carbon dioxide does the leaky faucet produce in a year?
- The speed of sound traveling through the sea is a function of temperature, salinity, and pressure. It is modeled by the function C = 1449.2 + 4.67T -0.055T² +0.00029T³ + (1.34-0.01T) (S-35) + 0.016D where C is the speed of sound (in meters per second), T is the temperature (in degrees Celsius), S is the salinity (the concentration of salts in parts per thousand, which means grams of dissolved solids per 1000 grams of water), and D is the depth below the sea surface, in meters. Calculate the following (Check attached image d3) when T = 10 °C, S = 35 parts per thousand, and D = 100 m. Explain the physical meaning of these derivatives.The Helmholtz free energy of a liquid column that rises, due to surface tension, inside a capillary tube (Figure 1), as a function of the height, h, is given by: F(h) =(ro)gr^2h^2/2 = -2 pi sigma r h cos teta, where r is the radius of the tube, g is the local ac- celaration of gravity, is the surface tension of the liquid, and is the contact angle of the liquid in contact with the wall of the tube. (a) From this expression, obtain the value of h as a function of the other physical parameters at equilibrium.Calculate the height that water will rise in a capil-lary of diameter 0.05mm. Assume that the contactangle between the water and the tube is zero. Thesurface tension of water at experimental conditionsisσ= 7.73×10−2N/m, and the local accelarationof gravity isg= 9.7m/s2.Thermodynamics Answer the following problem with complete solutions. Write legibly A balloon is filled with pure oxygen at 10 ℃. The balloon is released from the bottom of a water-filled testing pool and floats 30 m to the water surface (where the atmospheric pressure is standard). The volume of the balloon is 3,000 cm^3. The temperature is 25 ℃ at the surface of the water, and the water temperature at the bottom of the pool is 10 ℃. What is the volume of the balloon at the surface after it has come into thermal equilibrium with the surroundings