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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 → 2 → 3 → 4 → 1. Which ... 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
Which statement about this cycle is true?
Answer
In the context of the idealized diesel engine cycle, the correct statement is that 'Energy is supplied to the air by heating only in process 2 → 3.' This process represents the addition of heat to the system, while the other statements are not correct.
Step 2
Deduce whether these claims are true.
Answer
Claim A states an increase in work done per cycle of 130 J:
To evaluate this claim, we consider the area enclosed by the cycle in the modified diagram (Figure 4), representing the work done by the system during the cycle. The areas can be calculated based on the dimensions indicated in the diagrams, allowing us to confirm the increase. If the calculations yield an area of 130 J or above, Claim A is valid.
Claim B states an increase in efficiency of more than 15%:
Efficiency () can be defined as . Comparing the efficiency before and after modification can validate this claim. If the modified cycle's efficiency exceeds the initial by more than 15%, then Claim B is true.
Step 3
State the meaning of the terms Q and ΔU in this equation.
Answer
represents the total heat added to the system, indicating energy transfer into the system by heating. denotes the change in internal energy of the system, which quantifies the energy stored within the system, whether increasing or decreasing due to thermal dynamics.
Step 4
Calculate the energy that must be removed by cooling for process 5 → 1.
Answer
To find the energy removed, we can utilize the first law of thermodynamics: Here, given that , we must find , the work done. Since process 5 → 1 occurs at constant pressure, determine to complete the calculation. If this work yields a valid value, will be the energy needed to remove.
Assuming work done is known, we simply use the formula to derive accordingly.
Step 5
Determine the maximum temperature in the cycle.
Answer
To find the maximum temperature during the cycle, consider the ideal gas law and stages of the process. The temperature can be derived from the relationship: Utilize known volume, pressure, and the number of moles of gas involved at each state. Identify the highest pressure and volume combination to ascertain the maximum temperature correlating with that state.