Generated ERQ

## ERQ · 14 marks · Topics: E.4 Fission + A.3 Work, energy and power **Stem.** The Sizewell-C pressurised water reactor (PWR) is being commissioned with U-235 fuel enriched to 4.5%. At full operation, the core sustains a chain reaction releasing thermal energy at a rate of 3000 MW. Each fission of U-235 releases on average 200 MeV of usable energy. The thermal energy is removed by pressurised water at 320 °C, which transfers heat to a secondary loop driving steam turbines that generate electrical power at an overall thermal-to-electrical efficiency of 33%. Waste heat is rejected to seawater drawn from the North Sea at an intake temperature of 12 °C; environmental regulations require the outflow temperature to be no more than 22 °C. The seawater pumps lift the coolant through a vertical head of 8.5 m before it enters the condenser. ### Part (a) State [2 marks] · AO1 · Topic: E.4 State what is meant by a *chain reaction* in a nuclear fission reactor, and state the role of the moderator in a PWR. ### Part (b)(i) Show that [3 marks] · AO2 · Topic: E.4 Show that the number of U-235 fissions occurring per second in the core at full power is approximately 9.4 × 10¹⁹ s⁻¹. ### Part (b)(ii) Calculate [3 marks] · AO2/AO3 · Topic: E.4 The reactor operates continuously at full power for one calendar year (365 days). Calculate the mass of U-235 consumed by fission during this period. ### Part (c) Determine [3 marks] · AO3 · Topic: E.4 + A.3 The condenser rejects waste heat to seawater, which must not rise in temperature by more than 10 °C. Using the efficiency given in the stem, determine the minimum mass flow rate of seawater (in kg s⁻¹) required. (Specific heat capacity of seawater = 4.0 × 10³ J kg⁻¹ K⁻¹.) ### Part (d) Suggest [3 marks] · AO3 · ASSUMPTIONS DISCRIMINATOR The actual mass flow rate of seawater required in practice is significantly larger than the value calculated in (c). Suggest three reasons, grounded in the work–energy principle and the idealisations made in (c), why this is the case. --- ## Mark Scheme ### Part (a) [2 marks] - M1: Chain reaction = neutrons released by one fission go on to induce further fissions in other U-235 nuclei, sustaining the reaction [ECF: no] - M2: Moderator (water in PWR) slows down fast neutrons to thermal energies to increase fission cross-section / probability of further fission [ECF: no] ### Part (b)(i) [3 marks] - M1: Energy per fission converted: 200 × 10⁶ × 1.6 × 10⁻¹⁹ = 3.2 × 10⁻¹¹ J [ECF: no] - M2: Sets rate = P / E_fission with P = 3.0 × 10⁹ W [ECF: yes] - M3: 3.0 × 10⁹ / 3.2 × 10⁻¹¹ = 9.375 × 10¹⁹ ≈ 9.4 × 10¹⁹ s⁻¹ (must show > 2 sf to confirm) [ECF: yes] ### Part (b)(ii) [3 marks] - M1: Total fissions in year = 9.4 × 10¹⁹ × 365 × 24 × 3600 = 2.96 × 10²⁷ [ECF: yes from b(i)] - M2: Mass of one U-235 atom = 235 × 1.66 × 10⁻²⁷ = 3.90 × 10⁻²⁵ kg (or use molar mass route) [ECF: no] - M3: Mass consumed = 2.96 × 10²⁷ × 3.90 × 10⁻²⁵ ≈ 1.16 × 10³ kg ≈ 1.2 × 10³ kg (2 sf, units) [ECF: yes] ### Part (c) [3 marks] - M1: Waste thermal power = (1 − 0.33) × 3000 MW = 2.01 × 10⁹ W [ECF: no] - M2: Applies P = ṁ c ΔT, rearranged to ṁ = P / (c ΔT) with ΔT = 10 K [ECF: yes] - M3: ṁ = 2.01 × 10⁹ / (4.0 × 10³ × 10) = 5.0 × 10⁴ kg s⁻¹ (2 sf, correct units) [ECF: yes] ### Part (d) [3 marks] — award any THREE distinct reasons - M1: Pump must do additional work against gravity (lifting seawater through 8.5 m head) and against viscous/friction losses in pipework — this work input becomes additional thermal energy that the flow must carry away [ECF: no] - M2: Real mixing with ambient seawater is non-uniform / thermal plume forms, so the bulk outflow ΔT must be kept well below 10 °C to satisfy local regulation — requiring greater ṁ [ECF: no] - M3: The 33% efficiency is an idealised steady-state value; in practice additional thermal losses occur in pipework, turbine bleed, and auxiliary systems, so waste heat rejected at the condenser exceeds (1 − η)P [ECF: no] ### Marker notes - Alternative for (b)(ii): via molar route — moles = fissions/N_A = 4.92 × 10³ mol → mass = 4.92 × 10³ × 0.235 = 1.16 × 10³ kg. Accept 1.1–1.2 × 10³ kg. - (b)(i): "show that" requires candidate to reach a value with at least 2 sf and demonstrate it rounds to 9.4 × 10¹⁹; bare statement of answer scores M3 only if M1 and M2 working shown. - (c): accept range 4.9–5.1 × 10⁴ kg s⁻¹. - (d) discriminator: accept any three of — pump work against gravitational PE (mgh) of lifted seawater; viscous/friction work in pipes contributing heat; non-ideal mixing requiring sub-10 °C bulk rise; auxiliary thermal losses beyond the simple (1−η) model; finite heat-exchanger effectiveness preventing full ΔT utilisation; intake temperature variability requiring safety margin. Each reason must explicitly link to either additional energy input (work–energy) or to an idealisation in part (c).