Final answer:
To calculate the temperature at each compression stage and the heat that must be removed in the intercooling stage, use the relevant formulas and equations for adiabatic compression and intercooling. Calculate the temperature at the end of each stage using the appropriate formulas, and calculate the entropy generated in each stage using the entropy formula for adiabatic processes. Finally, calculate the heat that must be removed in the intercooling stage using the first law of thermodynamics.
Step-by-step explanation:
In order to calculate the temperature at the end of each compression stage, as well as the entropy generated and the amount of heat that must be removed in the intercooling stage, we need to use the relevant formulas and equations for adiabatic compression and intercooling.
- Compression Stage 1:
Using the adiabatic compression formula, we can calculate the temperature at the end of compression stage 1 as follows: T₁ = T₀ * (P₁ / P₀) ^ ((y-1) / y), where T₀ is the initial temperature, P₀ is the initial pressure, T₁ is the final temperature, P₁ is the final pressure, and y is the specific heat ratio for the gas (which is 7/5 for diatomic gases). Substitute the given values into the formula to calculate T₁. - Intercooling Stage:
To calculate the temperature at the end of the intercooling stage, we can use the ideal gas law formula: P₁ * V₁ / T₁ = P₂ * V₂ / T₂, where P₁ is the pressure before intercooling, V₁ is the volume before intercooling, T₁ is the temperature before intercooling, P₂ is the pressure after intercooling, V₂ is the volume after intercooling, and T₂ is the temperature after intercooling. Given the values P₁, V₁, T₁, P₂, and solve for T₂. - Compression Stage 2:
Using the adiabatic compression formula again, calculate the temperature at the end of compression stage 2 using the given values for P₃, V₃, T₂, P₄, and y.
For calculating the entropy generated in each stage, we need to apply the entropy formula for adiabatic processes: ∆S = Cᵥ * ln(T₂/T₁), where ∆S is the change in entropy, Cᵥ is the molar heat capacity at constant volume, and T₁ and T₂ are the initial and final temperatures of the stage, respectively. Calculate the entropy generated in each stage using the given values for Cᵥ and the corresponding temperatures.
Lastly, to calculate the amount of heat that must be removed in the intercooling stage, we can apply the first law of thermodynamics: Q = ∆U - W, where Q is the heat transfer, ∆U is the change in internal energy, and W is the work done. Calculate the work done using the adiabatic work formula for each compression stage, and substitute the values into the equation to find the heat that must be removed.