In an ideal heat-engine cycle a fixed mass of air is taken through the following four processes - AQA - A-Level Physics - Question 3 - 2019 - Paper 6

To find the temperature at point C, we can use the ideal gas law:

$PV = nRT$

where:

• P is the pressure,
• V is the volume,
• n is the number of moles,
• R is the ideal gas constant (approximately 8.31 J/(mol·K)),
• T is the temperature in Kelvin.

For process C:

• P_C = 1.0 × 10⁶ Pa,
• V_C = 13 × 10⁻³ m³.

Since the number of moles and R are constants, we can express the relationship across A, B, and C:

Using the data for point B where T_B = 295 K:

$P_A V_A = nRT_A ext{ and } P_C V_C = nRT_C$

Setting the ratios: $\frac{P_C V_C}{P_B V_B} = \frac{T_C}{T_B}$

Substituting values: $\frac{(1.0 × 10⁶ Pa) × (13 × 10⁻³ m³)}{(2.2 × 10⁵ Pa) × (4.1 × 10⁻² m³)} = \frac{T_C}{295 K}$

Now, calculate for T_C:

o T_C = 295 K × (\frac{(1.0 × 10⁶) × (13 × 10⁻³)}{(2.2 × 10⁵) × (4.1 × 10⁻²)})

After calculating, T_C is found to be approximately 420 K.

Based on the conditions of each process, the values can be summarized as:

Process	Work done W (J)	Energy transfer Q (J)
A → B	-7100	-7100
B → C	4000	+4000
C → D	10300	+10300
D → A	0	-1400

Note:

• Negative values indicate work done by the system, while positive values indicate work done on the system.