Figure 3 shows the $p-V$ diagram for an idealised diesel engine cycle - AQA - A-Level Physics - Question 3 - 2018 - Paper 6

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 $p-V$ 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.

$Q$ refers to the heat added to the system, which is energy transferred in by heat during the processes.

$riangle U$ refers to the change in internal energy of the system, indicating how the internal energy has changed as the system undergoes the thermodynamic processes.

Using the first law of thermodynamics:

$Q = riangle U + W$

Given that $riangle U = -374 J$ 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 $Q$. The energy removed by cooling is then:

For example, if work done $W$ was found to be say, X, then:

$Q = -374 J + X$

To find the maximum temperature in the cycle, apply the ideal gas law:

$PV = nRT$

Given the number of moles (0.060 mol), and substituting under the relevant conditions for the state that gives the highest $T$, we can isolate $T$ 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.