Answer :
Final answer:
The Otto cycle includes adiabatic compression, isochoric heating, adiabatic expansion, and isochoric cooling. The maximum temperature and pressure can be calculated using respective formulae, and thermal efficiency depends on the compression ratio and heat capacity ratio of air.
Explanation:
In the Otto cycle, the initial pressure P1 and temperature T1 are 103 kPa and 27°C, respectively. The heat added per kg of air Q_in is 1850 kJ, and the compression ratio r is 8. The maximum temperature can be calculated using the equation T2 = T1 * r^(γ-1), where γ is the heat capacity ratio, approximately 1.4 for air. The maximum pressure P2 can be found using the equation P2 = P1 * r^γ.
The thermal efficiency of the Otto cycle can be calculated using the formula η = 1 - (1 / r^(γ-1)). The P-V and T-S diagrams of the Otto cycle show four main stages: adiabatic compression, isochoric heating, adiabatic expansion, and isochoric cooling.
Note that the highest pressure and temperature occur at the end of the combustion process, and the thermal efficiency is inversely related to the compression ratio and the heat capacity ratio of air.
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Final answer:
In an Otto cycle, the maximum temperature and pressure occur at the end of the compression stroke. The maximum temperature is 1620K and the maximum pressure is 2927kPa. The thermal efficiency of the cycle is 56.3%.
Explanation:
In an Otto cycle, the maximum temperature and maximum pressure occur at the end of the compression stroke. To find the maximum temperature, we can use the relationship T2 = T1 imes (r)^(gamma-1), where T2 is the maximum temperature, T1 is the initial temperature, r is the compression ratio, and gamma is the specific heat ratio. Plugging in the values, we get T2 = 300K x 8^(1.4-1) = 1620K. The maximum pressure can be found using the relationship P2 = P1 imes (r)^(gamma), where P2 is the maximum pressure and P1 is the initial pressure. Plugging in the values, we get P2 = 103kPa x 8^(1.4) = 2,927kPa.
The thermal efficiency of the cycle can be calculated using the formula efficiency = 1 - (1/r)^(gamma-1), where r is the compression ratio and gamma is the specific heat ratio. Plugging in the values, we get efficiency = 1 - (1/8)^(1.4-1) = 0.563, or 56.3%.
This information can be represented in the P-V and T-S diagrams of the Otto cycle. The P-V diagram will show a compression stroke from state 1 to state 2, followed by an expansion stroke from state 3 to state 4. The T-S diagram will show a constant volume heat addition from state 2 to state 3, followed by a constant volume heat rejection from state 4 to state 1. These diagrams will depict the changes in pressure, volume, temperature, and entropy throughout the cycle.
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