a. A heat engine is a device that converts thermal energy into mechanical work. An internal combustion engine is a type of heat engine where the combustion of fuel takes place internally, within the engine itself. The fuel is burnt in a combustion chamber and the resulting hot gases expand and push a piston, generating mechanical work. An external combustion engine, on the other hand, is a type of heat engine where the combustion of fuel takes place outside the engine. In this case, the heat from the combustion is transferred to a working fluid, which expands and performs mechanical work in the engine.
b. To determine the values for the state variables at the end of each thermodynamic process in the cycle, we'll use the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.
1. Solar thermal heating (sochorie process): The gas is heated from an initial temperature of 6.06 MPa to the final temperature of 102°C. The pressure remains constant, so the process is isobaric. Using the ideal gas law, we can determine the volume:
V1 = (nRT1) / P1
2. Isothermal expansion process: The gas expands isothermally from the pressure of 6.06 MPa to 4.65 MPa. Since the process is isothermal, the temperature remains constant. Using the ideal gas law, we can determine the volume:
V2 = (nRT1) / P2
3. Anusochoric process: The temperature remains constant, but the volume changes. Since the process is not isobaric, we can't use the ideal gas law directly. Instead, we need additional information or assumptions to determine the change in volume.
4. Isothermal compression process: The gas is compressed isothermally from the pressure of 4.65 MPa to the initial pressure of 6.06 MPa. Since the process is isothermal, the temperature remains constant. Using the ideal gas law, we can determine the volume:
V4 = (nRT1) / P4
c. To determine the work done per cycle, we can use the equation:
W = Qh - Qc
where Qh is the heat absorbed from the high temperature reservoir and Qc is the heat rejected to the low temperature reservoir. Since the engine is reversible, the heat transferred in each process is proportional to the corresponding temperature change:
Qh = nCv(T3 - T2)
Qc = nCv(T4 - T1)
where Cv is the molar specific heat at constant volume.
d. To determine the mass of water that can be converted into ice per cycle, we need to calculate the heat removed from the water. The heat removed is given by:
Qc = mcΔHf
where mc is the mass of water and ΔHf is the specific latent heat of fusion of water. We can then equate this to the heat rejected by the engine:
Qc = nCv(T4 - T1)
Solving for mc:
mc = (nCv(T4 - T1)) / ΔHf
e. The Stirling engine described above is different from Diesel and Otto engines in several ways:
1. Working principle: The Stirling engine operates on the Stirling cycle, which involves cyclic compression and expansion of a fixed amount of gas. The expansion and compression are driven by changes in temperature. In contrast, Diesel and Otto engines operate on the principles of internal combustion, where fuel is combusted inside the engine to create high-pressure gases that drive the piston.
2. Fuel type: The Stirling engine can operate on any external heat source, including solar energy, biomass, or fossil fuels. Diesel engines operate on diesel fuel, while Otto engines operate on gasoline.
3. Efficiency: Stirling engines tend to have lower thermal efficiency compared to Diesel and Otto engines, primarily due to the temperature differences involved in the Stirling cycle. Diesel and Otto engines can achieve higher thermal efficiency through direct combustion of fuel.
4. Emissions: Stirling engines have low emissions since the combustion of fuel occurs outside the engine, resulting in cleaner exhaust gases. In contrast, Diesel and Otto engines produce emissions as a result of the combustion process.
Overall, each type of engine has its advantages and disadvantages, and their suitability depends on the specific application and requirements.
You have been requested to design a Stirling heat engine that uses sunlight to heat 2.7 kg of helium gas (molar mass-4.0026 g) initially at 6.06 MPa, to 102°C and a cold mountain stream to cool the gas back down to 2°C. The working fluid undergoes a Stirling cycle that begins with ((sochorie solar thermal heating of the fluid followed by sothermal expansion of the fluid to a pressure of 4.65 MPa. Next, the fluid is restored to its original temperature by anusochoric process. Finally, its original volume and pressure are restored by undergoing isothermal compression.
a. By defining a heat engine, distinguish internal and external combustion engines.
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b. Modeling the working fluid as an ideal gas, determine the values for the state
variables (P. V and T) at the end of each thermodynamic process in the cycle. The
ideal gas constant, R, is 8.31 J.mol' K
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c. Assuming the engine is reversible and 4184 J of heat is absorbed from the high temperature reservoir in one cycle, how much work is done per cycle?
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d. You intend to use the energy produced by the solar engine to work a refrigerator
that has a coefficient of performance of 2.75. What mass of water, originally at 0°C, can be converted into ice at 0°Cper cycle? Specific latent heat of fusion of water is 334 kJ.kg¹.
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e. By explaining the processes involved, distinguish the Stirling engine described above from Diesel and Otto Engines.
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