An electric heater is rated at 500 W. a. How much energy is delivered to the heater in half an h

step 1 In the given problem we have been given an electric heater which is rated at 500 watt means its

An electric heater is rated at 500 W. a. How much energy is...

An electric heater is rated at $500 \mathrm{W}$. a. How much energy is delivered to the heater in half an hour? b. The heater is being used to heat a room containing $50 \mathrm{kg}$ of air. If the specific heat of air is $1.10 \mathrm{kJ} / \mathrm{kg} \cdot^{\circ} \mathrm{C},$ and 50 percent of the thermal energy heats the air in the room, what is the change in air temperature in half an hour? c. At $\$ 0.08$ per kWh, how much does it cost to run the heater $6.0 \mathrm{h}$ per day for 30 days?

An electric heater is rated at $500 \mathrm{W}$.
a. How much energy is delivered to the heater in half an hour?
b. The heater is being used to heat a room containing $50 \mathrm{kg}$ of air. If the specific heat of air is $1.10 \mathrm{kJ} / \mathrm{kg} \cdot^{\circ} \mathrm{C},$ and 50 percent of the thermal energy heats the air in the room, what is the change in air temperature in half an hour?
c. At $\$ 0.08$ per kWh, how much does it cost to run the heater $6.0 \mathrm{h}$ per day for 30 days?

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Key Concepts

Electrical Power and Energy

Electrical power is defined as the rate at which energy is used or converted, measured in watts (joules per second). The energy delivered or consumed by a device is determined by multiplying its power rating by the time it operates, which is essential in calculating the total energy input over a period.

Unit Conversions

Many problems require converting between different units such as hours to seconds or joules to kilowatt-hours. Accurate conversion of these units is crucial in ensuring that the energy and power calculations align correctly with the physical quantities being measured.

Specific Heat Capacity

Specific heat capacity is a property of a material that indicates the amount of energy required to raise the temperature of one kilogram of the substance by one degree Celsius. This concept is central when determining how much a material's temperature changes based on the heat it absorbs or loses.

Thermal Energy Transfer and Efficiency

Thermal energy transfer involves the movement of heat energy from one system to another. In practical applications, not all the energy delivered is used effectively due to losses or inefficiencies. Accounting for the efficiency of the energy transfer is important when calculating the resultant temperature change or overall energy usage cost.

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