# Step-by-Step Solutions --- ## 1. Energy Conversion ### (a) Convert MJ to Btu **Conversion factor:** - \( 1 \text{ MJ} = 947.817 \text{ Btu} \) **Calculation:** \[ 5 \text{ MJ} \times 947.817 \frac{\text{Btu}}{\text{MJ}} = 4739.09 \text{ Btu} \] **Final Answer:** - **5 MJ = 4,739 Btu** --- ### (b) Convert 4 barrels of oil to kWh **Conversion factors:** - \( 1 \text{ barrel oil} = 5.8 \text{ million Btu} \) - \( 1 \text{ Btu} = .000293071 \text{ kWh} \) **Step 1: Total Btu** \[ 4 \text{ barrels} \times 5.8 \times 10^6 \text{ Btu/barrel} = 23.2 \times 10^6 \text{ Btu} \] **Step 2: Convert to kWh** \[ 23,200,000 \text{ Btu} \times .000293071 \frac{\text{kWh}}{\text{Btu}} = 6,797.25 \text{ kWh} \] **Final Answer:** - **4 barrels of oil = 6,797 kWh** --- ## 2. Energy Usage Per Person in the U.S. Given: - Total U.S. energy use: 100 Quadrillion Btu/year - Population: 325 million - \( 1 \text{ quadrillion} = 10^{15} \) **Total Energy:** \[ 100 \times 10^{15} \text{ Btu} \] **Energy per person:** \[ \frac{100 \times 10^{15} \text{ Btu}}{325 \times 10^6 \text{ people}} = 307,692,308 \text{ Btu/person/year} \] ### (a) In MMBtu - \( 1 \text{ MMBtu} = 1,000,000 \text{ Btu} \) \[ \frac{307,692,308 \text{ Btu}}{1,000,000} = 307.7 \text{ MMBtu/person/year} \] ### (b) In MJ - \( 1 \text{ Btu} = 1.05506 \text{ kJ} \) - \( 1 \text{ MJ} = 1,000 \text{ kJ} \) \[ 307,692,308 \text{ Btu} \times 1.05506 = 324,234,204 \text{ kJ} \] \[ \frac{324,234,204}{1,000} = 324,234 \text{ MJ/person/year} \] ### (c) In MWh - \( 1 \text{ Btu} = .000293071 \text{ kWh} \) - \( 1 \text{ MWh} = 1,000 \text{ kWh} \) \[ 307,692,308 \text{ Btu} \times .000293071 = 90,231 \text{ kWh} \] \[ \frac{90,231}{1,000} = 90.2 \text{ MWh/person/year} \] --- **Final Answers:** - (a) **307.7 MMBtu/person/year** - (b) **324,234 MJ/person/year** - (c) **90.2 MWh/person/year** --- ## 3. Energy Use vs. Power ### Average Power Used per Person (in J/s) **Step 1: Find MJ/year per person from above:** \( 324,234,204 \text{ kJ} = 324,234,204,000 \text{ J} \) **Step 2: Number of seconds in a year:** \( 365 \times 24 \times 360 = 31,536,000 \) s **Step 3: Power (J/s):** \[ \frac{324,234,204,000 \text{ J}}{31,536,000 \text{ s}} = 10,288 \text{ J/s} \] **Final Answer:** - **Average power = 10,288 J/s (W) per person** ### Explanation: Energy vs. Power - **Energy** is the total amount of work done or heat transferred (measured in Joules, kWh, etc.). - **Power** is the *rate* at which energy is used or transferred (measured in Watts, or J/s). **In words:** Energy tells you how much you have used in total, while power tells you how fast you are using it at any instant. --- ## 4. Energy Use, Lightbulbs and Microwaves Given: - Home uses 83,835 kJ per day ### (a) 100 W Lightbulbs **Step 1: Convert kJ to kWh** \[ 83,835 \text{ kJ} \div 3,600 = 23.29 \text{ kWh/day} \] **Step 2: Energy used by one 100 W bulb in 24 hours** \[ 100 \text{ W} \times 24 \text{ h} = 2,400 \text{ Wh} = 2.4 \text{ kWh} \] **Step 3: Number of bulbs** \[ \frac{23.29 \text{ kWh}}{2.4 \text{ kWh/bulb}} = 9.70 \] **Final Answer:** - **You could run 9 full 100 W lightbulbs for 24 hours.** --- ### (b) 1,000 W Microwave **Step 1: How many hours will 23.29 kWh run a 1,000 W (1 kW) microwave?** \[ \frac{23.29 \text{ kWh}}{1 \text{ kW}} = 23.29 \text{ hours} \] **Final Answer:** - **The microwave would run for 23.29 hours.** --- ### (c) Annual Usage: 84,000 kJ/day to kWh/year **Step 1: Daily kWh** \[ 84,000 \text{ kJ} \div 3,600 = 23.33 \text{ kWh/day} \] **Step 2: Annual kWh** \[ 23.33 \text{ kWh/day} \times 365 = 8,515 \text{ kWh/year} \] **Explanation:** - Each day, the house uses about 23.33 kWh. - Over a year, this totals about 8,515 kWh, close to the stated value of 8,500 kWh/year. --- ## Summary Table | Conversion/Calculation | Value/Result | |------------------------------------------|-----------------------| | 5 MJ to Btu | 4,739 Btu | | 4 barrels oil to kWh | 6,797 kWh | | Per person, per year: | | | ... in MMBtu | 307.7 MMBtu | | ... in MJ | 324,234 MJ | | ... in MWh | 90.2 MWh | | Average power (J/s) per person | 10,288 J/s (W) | | 100 W bulbs, 24h, 83,835 kJ/day | 9 bulbs | | 1,000 W microwave, hours on 83,835 kJ | 23.29 hours | | 84,000 kJ/day to kWh/year | 8,515 kWh/year | --- **Note:** - For Btu, M = 1,000 (not million); for Joules, M = 1,000,000. - Use appropriate conversion factors for precise answers. - Always check units during conversions.