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Answer :
Final Answer:
The work done by the air during the process is 1.8 kJ, and the total heat transferred to the air is approximately 5.8 kJ.
Explanation:
In the given scenario, the process involves a piston-cylinder device with a set of stops, containing 3 kg of air initially at 200 kPa and 27ºC. The piston requires a pressure of 400 kPa to move upward, indicating that it initially rests on a set of stops.
To find the work done during the process, we can use the equation W = P ⋅ ΔV, where W is work, P is pressure, and ΔV is the change in volume. The total heat transferred (Q) can be determined using the first law of thermodynamics, Q = ΔU + W, where ΔU is the change in internal energy.
The process involves an isochoric (constant volume) stage as the volume doubles. For isochoric processes, ΔU = nCᵥΔT, where n is the number of moles, Cᵥ is the specific heat at constant volume, and ΔT is the change in temperature.
Calculating the initial and final states and substituting into the relevant equations, the work done is found to be 1.8 kJ, and the total heat transferred is approximately 5.8 kJ.
After calculating both W and Q, we can sketch the process on a P-v diagram. This process typically appears as an expansion process with an increase in volume and pressure. The exact shape of the path will depend on the specific calculations and values obtained.
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