Convert commercial unit of energy
Scenario
Aapke ghar ka bijli ka bill har mahine aata hai, jismein likha hota hai '`250 units` consumed'.
Ye 'unit' physics ki language mein kitne Joules ke barabar hota hai, aur bijli board Joules mein charge kyun nahi karta?
Mental model
Joule bohot chota chillar (coins) hai aur `kWh` badda note (currency) hai. Ghar ki electricity units `kWh` mein hoti hain.
Ek Joule energy bohot hi kam hoti hai (ek choti torch ko fraction of second chalane bhar). Ghar ka TV aur AC mahino chalte hain. Toh Joules mein bill banayenge toh arabo (billions) mein numbers aayenge. Isliye unit badal kar kilowatt-hour (`kWh`) kar di jati hai.
Explanation
Energy ki standard SI unit Joule (`J`) hoti hai, jo day-to-day electrical consumption measure karne ke liye bahut chhoti aur inconvenient hai. Isliye commercial purposes ke liye ek badi unit ka use kiya jata hai jise 'kilowatt-hour' ya `kWh` kehte hain. Ghar ke bill mein ise hi simply 'unit' bulaya jata hai (matlab `1 unit = 1 kWh`).
`1 kWh` ka exact meaning kya hai? Agar ek machine (jaise bada heater) jiski power `1 kilowatt` (yani `1000 W`) hai, aur aap use lagatar `1 hour` (ek ghanta) chalate ho, toh wo exact `1 kWh` energy consume karegi.
Ab iska Joule ke saath relation banate hain:
`1 kilowatt = 1000 W` (yani `1000 J/s`)
`1 hour = 3600 s`
Toh, `1 kWh = 1 kW imes 1 h`
`= 1000 W imes 3600 s`
`= 3,600,000 Joules`.
Standard form mein isko hum `3.6 imes 10^6 J` likhte hain. Ye conversion directly exam mein poocha jata hai aur numericals solve karne mein bhi kaam aata hai.
Worked example
Problem: A radio set of `60 W` runs for `50 hours`. How much electrical energy is consumed in `kWh`?
- `kWh` nikalne ke liye Power (kilowatt mein) ko Time (hours mein) se multiply karna padta hai. Pehle power ko convert karo.
- Time already hours mein hai.
- Energy `P imes t` karke nikal lo.
Answer: `3 kWh`
Problem: An electric heater is rated `1500 W`. How much energy does it use in `10 hours`? Give the answer in Joules and `kWh`.
- Pehle Power ko kilowatt aur Time ko hours mein likh kar `kWh` mein nikalte hain.
- `kWh` mein energy hogi:
- Ab `1 kWh = 3.6 imes 10^6 J` ka logic use karke Joules nikal lo.
Answer: `15 kWh` or `5.4 imes 10^7 J`
Key points
- Commercial Unit: The commercial unit of electrical energy is kilowatt-hour (`kWh`).
- Conversion Value: `1 kWh = 3.6 imes 10^6 J`.
Common mistakes
- Thinking kWh is a unit of Power: Kyunki naam mein 'kilowatt' aata hai, bohot log isko power ka unit samajh lete hain. Lekin dhyan se dekho, ye kilowatt multiplied by time (hour) hai (`Power imes Time = Energy`). Ye Energy ka unit hai, strictly.
Recall questions
- What is the relation between kilowatt-hour (kWh) and Joule (J)?
- What physical quantity is measured in kilowatt-hour (kWh)?
- How many seconds are there in 1 hour?
Questions & answers
A certain household has consumed 250 units of energy during a month. How much energy is this in joules?
9 x 10^8 J
Approach: Multiply 250 by 3.6 x 10^6. (250 * 3.6 = 900), so 900 * 10^6 = 9 * 10^8.
Express 1 kWh in joules.
3.6 x 10^6 J
Approach: 1 kW = 1000 W and 1 h = 3600 s. So 1000 W * 3600 s = 3,600,000 J.
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