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Figure 3 shows the $p-V$ diagram for an idealised diesel engine cycle - AQA - A-Level Physics - Question 3 - 2018 - Paper 6
Question 3
Figure 3 shows the $p-V$ diagram for an idealised diesel engine cycle. In this cycle a fixed mass of air is taken through four processes 1 $ ightarrow$ 2 $ ightarrow... show full transcript
Worked Solution & Example Answer:Figure 3 shows the $p-V$ diagram for an idealised diesel engine cycle - AQA - A-Level Physics - Question 3 - 2018 - Paper 6
Step 1
Step 2
Deduce whether these claims are true.
Answer
To evaluate the claims regarding the modified cycle:
- Claim A: The work done per cycle has increased by 130 J. The area under the curve on the diagram (Figure 4) was larger than in Figure 3, making the claim valid upon evaluating the respective areas.
- Claim B: The efficiency has increased by more than 15%. We can compare the efficiencies by evaluating the areas under the respective curves and ensuring the claim holds by calculations. Since areas are based on the input and output work, a percentage increase would confirm the claim.
Step 3
State the meaning of the terms Q and ΔU in this equation.
Answer
refers to the heat added to the system, which is energy transferred in by heat during the processes.
refers to the change in internal energy of the system, indicating how the internal energy has changed as the system undergoes the thermodynamic processes.
Step 4
Calculate the energy that must be removed by cooling for process 5 → 1.
Answer
Using the first law of thermodynamics:
Given that and knowing work done (which could be determined or assumed if not provided), we calculate:
If the work done in process 5 → 1 is known, we can rearrange this to solve for . The energy removed by cooling is then:
For example, if work done was found to be say, X, then:
Step 5
Determine the maximum temperature in the cycle.
Answer
To find the maximum temperature in the cycle, apply the ideal gas law:
Given the number of moles (0.060 mol), and substituting under the relevant conditions for the state that gives the highest , we can isolate as follows:
T = rac{PV}{nR}
By using the pressure and volume from the appropriate region of the cycle (say at process 3 to 4), we can deduce the maximum temperature.