A “60-watt equivalent” LED lightbulb is rated at 7.5 W and 800 lumens. How much power goes into light? (The rest goes into heat.)

Verified step by step guidance

1. Understand the problem: The LED lightbulb is rated at 7.5 W, meaning it consumes 7.5 watts of electrical power. Out of this, some portion of the power is converted into light (800 lumens), and the rest is converted into heat. We need to determine how much power is converted into light.
2. Recall the concept of luminous efficacy: Luminous efficacy is a measure of how efficiently a light source converts electrical power into visible light. It is typically expressed in lumens per watt (lm/W). For this problem, we need to calculate the luminous efficacy of the bulb using the given values.
3. Calculate the luminous efficacy: Use the formula for luminous efficacy: $E=\frac{L}{P}$, where $E$ is luminous efficacy, $L$ is the luminous output (800 lumens), and $P$ is the total power consumed (7.5 W).
4. Determine the fraction of power converted into light: Once the luminous efficacy is calculated, compare it to the theoretical maximum luminous efficacy for visible light (approximately 683 lm/W for monochromatic light at 555 nm). This comparison helps estimate the efficiency of the bulb and the fraction of power converted into light.
5. Subtract the power converted into light from the total power: The remaining power is converted into heat. Use the relationship $P=P$_total-P_light, where $P$_light is the power converted into light and $P$_total is the total power consumed (7.5 W).

Key Concepts

Power Rating

The power rating of a lightbulb, measured in watts (W), indicates the amount of electrical energy it consumes per unit time. In this case, the LED lightbulb is rated at 7.5 W, meaning it uses 7.5 joules of energy every second. Understanding this concept is crucial for determining how much energy is converted into light versus heat.

Luminous Flux

Luminous flux, measured in lumens, quantifies the total amount of visible light emitted by a source. The 800 lumens rating of the LED bulb indicates its brightness. This concept is essential for evaluating the efficiency of the bulb, as it relates the amount of light produced to the power consumed.

Efficiency

Efficiency in lighting refers to the ratio of useful light output (in lumens) to the power input (in watts). It can be calculated by dividing the luminous flux by the power rating. For the LED bulb, understanding its efficiency helps determine how much of the electrical energy is converted into light versus wasted as heat, which is critical for energy-saving assessments.