nie.co.uk/aqa-qb/ad515915-6499-4556-bb4e-73ea2f20afb9.png)\n\nThe student obtains the following data:\n* **Energy input to the heater:** \$18\\,000\\text{ J}\$\n* **Increase in thermal energy store of the oil:** \$13\\,500\\text{ J}\$","difficulty":6,"difficultyBand":"medium","totalMarks":9,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"ad17e6f5-a770-4b68-8c01-bef8009f192d","label":"a","content":"Use this data to calculate the efficiency of the heater.","markscheme":"- Recalls or uses $\\text{Efficiency} = \\frac{\\text{Useful energy output}}{\\text{Total energy input}}$ M1\n- Calculates $\\text{Efficiency} = \\frac{13\\,500}{18\\,000} = 0.75$ (or $75\\%$) A1","marks":2,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"efficiency_calculation","label":"Calculate efficiency","steps":[{"type":"text","order":0,"title":"Identify useful energy","content":"The **useful energy output** is the energy that heats the oil: its increase in thermal energy store. The **total energy input** is the energy supplied to the heater.","highlights":[{"text":"**Increase in thermal energy store of the oil:** \$13\\,500\\text{ J}\$","location":"specification"},{"text":"**Energy input to the heater:** \$18\\,000\\text{ J}\$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\text{efficiency}=\\frac{\\text{useful energy output}}{\\text{total energy input}}"},{"latex":"\\text{efficiency}=\\frac{13\\,500\\ \\text{J}}{18\\,000\\ \\text{J}}"},{"latex":"\\text{efficiency}=0.75=75\\%"}]},"order":1,"title":"Apply the efficiency formula","description":"Efficiency is the fraction of the input energy transferred usefully to the oil. Writing the formula earns the first mark. Substituting the two energies and obtaining 0.75 (or 75%) earns the second mark; efficiency has no unit."}]}],"generatedAt":"2026-07-22T12:16:17.177Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]},{"id":"1be0f794-8041-45c7-873c-c9abeba2a6c8","label":"b","content":"The heater is used for \$6\$ minutes. Calculate the power of the heater. Use the equation:\n\\[\\text{energy transferred} = \\text{power} \\times \\text{time}\\]","markscheme":"- Converts time from minutes to seconds: $6 \\times 60 = 360\\text{ s}$ B1\n- Recalls or uses $\\text{Power} = \\frac{\\text{Energy transferred}}{\\text{Time}}$ M1\n- Calculates $\\text{Power} = \\frac{18\\,000}{360} = 50\\text{ W}$ A1","marks":3,"order":1,"markingRubric":null,"explanation":{"methods":[{"id":"energy_time_power","label":"Energy divided by time","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=start}{\\color{@sky}{6\\ \\mathrm{min}}}\\times\\htmlData{anchor=sixty}{\\color{@orange}{60\\ \\mathrm{s\\,min^{-1}}}}"},{"latex":"\\htmlData{anchor=seconds}{\\color{@green}{360\\ \\mathrm{s}}}"}],"connections":[{"to":"seconds","from":"sixty","color":"sky","label":"multiply by 60"}]},"order":1,"title":"Convert the time","description":"Power uses joules per second, so time must be in seconds. Writing 6 × 60 = 360 s earns the B1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\text{energy transferred}=\\text{power}\\times\\htmlData{anchor=time}{\\text{time}}"},{"latex":"\\htmlData{anchor=formula}{\\color{@green}{\\text{power}=\\dfrac{\\text{energy transferred}}{\\text{time}}}}"}],"connections":[{"to":"formula","from":"time","color":"green","label":"divide by time"}]},"order":2,"title":"Rearrange the equation","description":"Make power the subject by dividing the energy transferred by the time. This earns the M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\mathrm{power}=\\frac{\\mathrm{energy\\ transferred}}{\\mathrm{time}}"},{"latex":"\\mathrm{power}=\\frac{\\htmlData{anchor=energy}{\\color{@sky}{18\\,000\\ \\mathrm{J}}}}{\\htmlData{anchor=time}{\\color{@orange}{360\\ \\mathrm{s}}}}"},{"latex":"\\htmlData{anchor=answer}{\\color{@green}{\\mathrm{power}=50\\ \\mathrm{W}}}"}],"connections":[{"to":"answer","from":"energy","color":

Power and efficiency

Question 15

Power and efficiency Questions

Power and efficiency

Question 15

Power and efficiency Questions