Question
I'm a physics student working on a problem set involving energy conversion. I need to calculate the amount of energy lost to heat and converted into light for a 100W incandescent bulb operating at 20% efficiency after 1.5 hours. Can you find a similar question on the website that provides a step-by-step solution or explanation?
Answers
GPT-4o mini
While I can't browse the internet in real-time to find specific questions or solutions, I can certainly help you work through the problem step by step.
### Problem Overview:
You have a 100W incandescent bulb operating at 20% efficiency. You want to calculate the energy lost to heat and converted into light over a period of 1.5 hours.
### Step-by-Step Solution:
1. **Calculate the total energy consumed by the bulb:**
The power rating of the bulb is 100 W, and you want to find the total energy consumed over 1.5 hours.
\[
\text{Total Energy (E)} = \text{Power (P)} \times \text{Time (t)}
\]
Convert time from hours to seconds:
\[
t = 1.5 \, \text{hours} \times 3600 \, \text{seconds/hour} = 5400 \, \text{seconds}
\]
Now calculate the total energy:
\[
E = 100 \, \text{W} \times 5400 \, \text{seconds} = 540000 \, \text{Joules}
\]
2. **Calculate the useful energy output (converted into light):**
The efficiency of the bulb is 20%. Thus, the useful energy output (light energy) can be calculated as:
\[
\text{Useful Energy (E}_{\text{useful}}) = \text{Efficiency} \times \text{Total Energy}
\]
\[
E_{\text{useful}} = 0.20 \times 540000 \, \text{J} = 108000 \, \text{J}
\]
3. **Calculate the energy lost to heat:**
The energy lost to heat can be found by subtracting the useful energy output from the total energy consumed:
\[
\text{Energy Lost to Heat (E}_{\text{heat}}) = \text{Total Energy} - \text{Useful Energy}
\]
\[
E_{\text{heat}} = 540000 \, \text{J} - 108000 \, \text{J} = 432000 \, \text{J}
\]
### Summary of Results:
- Total energy consumed by the bulb over 1.5 hours: **540000 J**
- Useful energy converted into light: **108000 J**
- Energy lost as heat: **432000 J**
If you need any further help or additional explanations, feel free to ask!
### Problem Overview:
You have a 100W incandescent bulb operating at 20% efficiency. You want to calculate the energy lost to heat and converted into light over a period of 1.5 hours.
### Step-by-Step Solution:
1. **Calculate the total energy consumed by the bulb:**
The power rating of the bulb is 100 W, and you want to find the total energy consumed over 1.5 hours.
\[
\text{Total Energy (E)} = \text{Power (P)} \times \text{Time (t)}
\]
Convert time from hours to seconds:
\[
t = 1.5 \, \text{hours} \times 3600 \, \text{seconds/hour} = 5400 \, \text{seconds}
\]
Now calculate the total energy:
\[
E = 100 \, \text{W} \times 5400 \, \text{seconds} = 540000 \, \text{Joules}
\]
2. **Calculate the useful energy output (converted into light):**
The efficiency of the bulb is 20%. Thus, the useful energy output (light energy) can be calculated as:
\[
\text{Useful Energy (E}_{\text{useful}}) = \text{Efficiency} \times \text{Total Energy}
\]
\[
E_{\text{useful}} = 0.20 \times 540000 \, \text{J} = 108000 \, \text{J}
\]
3. **Calculate the energy lost to heat:**
The energy lost to heat can be found by subtracting the useful energy output from the total energy consumed:
\[
\text{Energy Lost to Heat (E}_{\text{heat}}) = \text{Total Energy} - \text{Useful Energy}
\]
\[
E_{\text{heat}} = 540000 \, \text{J} - 108000 \, \text{J} = 432000 \, \text{J}
\]
### Summary of Results:
- Total energy consumed by the bulb over 1.5 hours: **540000 J**
- Useful energy converted into light: **108000 J**
- Energy lost as heat: **432000 J**
If you need any further help or additional explanations, feel free to ask!