Net work: 1025 kJ/kg, Thermal efficiency: 0.5125, Mean effective pressure: 400 kPa, Maximum temperature: 2966.67 K.
(a) Net work produced during each cycle
The net work produced during each cycle is equal to the difference between the work done during the expansion process and the work done during the compression process. The work done during each process can be calculated using the following formula:
W = nRT ln(V2/V1)
where:
W is the work done (in kJ)
n is the number of moles of gas
R is the gas constant (in kJ/mol·K)
T is the temperature (in K)
V is the volume (in m³)
We can use the ideal gas law to relate the pressure, volume, and temperature of the gas:
PV = nRT
We can also use the fact that the compression ratio is 8 to relate the volumes at the beginning and end of the compression process:
V2 = 8V1
Using these equations, we can calculate the work done during the compression process:
WC = nRT ln(8V1/V1) = 3nRT ln(8)
We can also calculate the work done during the expansion process:
WE = nRT ln((V2/V1)/(8/1)) = 3nRT ln(1/8)
The net work produced during each cycle is then:
WN = WE - WC = 6nRT ln(1/8)
(b) Thermal efficiency of the cycle
The thermal efficiency of the cycle is equal to the ratio of the net work produced during each cycle to the heat added during the combustion process:
η = WN/QH = (6nRT ln(1/8)) / (1200 kJ)
(c) Mean effective pressure
The mean effective pressure (MEP) is a measure of the average pressure acting on the piston during the power stroke. It is calculated using the following formula:
MEP = W / Vd
where:
W is the net work produced per kg of air (in kJ/kg)
Vd is the displacement volume (in m³/kg)
The displacement volume is the volume of air that is displaced by the piston during one stroke. It is equal to the stroke volume divided by the mass of air in the cylinder.
Vd = Vs / m
where:
Vs is the stroke volume (in m³)
m is the mass of air in the cylinder (in kg)
The stroke volume is typically provided in the engine specifications. The mass of air in the cylinder can be calculated using the ideal gas law
m = PV / RT
(d) Maximum temperature
The maximum temperature is reached at the end of the combustion process. We can use the ideal gas law to relate the temperature and pressure at this point:
Tv = Pv / (nRv)
where:
Tv is the maximum temperature (in K)
Pv is the pressure at the end of the combustion process (in kPa)
v is the specific volume (in m³/kg)
The specific volume can be calculated using the following equation:
v = V / m
where:
V is the volume at the end of the combustion process (in m³)
m is the mass of air in the cylinder (in kg)