(a) A particular household uses a 2.2-kW heater 2.0 h/day...

($a$) A particular household uses a 2.2-kW heater 2.0 h/day ("on" time), four 100-W lightbulbs 6.0 h/day, a 3.0-kW electric stove element for a total of 1.0 h/day and miscellaneous power amounting to 2.0 kWh/day. If electricity costs $\$$0.115 per kWh, what will be their monthly bill (30 d)? ($b$) How much coal (which produces 7500kcal/kg ) must be burned by a 35%-efficient power plant to provide the yearly needs of this household?

Key Concepts

Energy Consumption Calculation

This concept involves determining the amount of energy used by an appliance or system over time by multiplying the device's power rating (in kilowatts) by the time it is in operation (in hours). It is a fundamental step in quantifying energy usage, which is often expressed in kilowatt-hours (kWh). This calculation is essential for understanding household energy demands and forms the basis of many further analyses in energy studies.

Electricity Cost Calculation

Once the total energy consumption in kWh is determined, the cost calculation involves multiplying this consumption by the price per kWh charged by the utility provider. This concept links quantitative energy usage to monetary cost, allowing households and businesses to manage budgets and evaluate energy-saving measures based on their cost impacts.

Energy Unit Conversion

Different energy units such as kilowatt-hours (kWh), calories, and joules are used in various contexts. Understanding how to convert between these units is crucial, especially when comparing electrical energy to thermal energy outputs from fuel consumption. This conversion ensures that the energy produced by combustion (often given in kilocalories or joules) can be accurately related to the energy requirements of electrical systems.

Fuel Energy Content

Fuel energy content, or energy density, indicates how much energy is released per unit mass of fuel when it is burned. In this context, knowing the calorific value of coal (e.g., 7500 kcal/kg) is essential for determining the amount of fuel needed to generate a specified amount of energy. This concept is critical in energy resource management and environmental assessments of fuel usage.

Thermal Efficiency

Thermal efficiency refers to the ratio of useful work or energy output to the total energy input from fuel. In power plants, it quantifies how well the plant converts the energy stored in fuel into electrical energy, taking into account losses due to heat and other inefficiencies. This concept helps in understanding the real-world performance of power generation systems and is key when calculating the amount of fuel required to meet specific energy demands.

Transcript

Please give Ace some feedback