1 joule = …………. erg

Options

A. `10^(5)`
B. `10^(-5)`
C. `10^(-7)`
D. `10^(7)`

Answer

To convert joules to ergs, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Units**:
- 1 Joule (J) is the SI unit of energy.
- 1 Erg (erg) is the CGS (centimeter-gram-second) unit of energy.

2. **Express Joules in Basic Units**:
- The joule can be expressed in terms of basic physical quantities:
\[ 1 \text{ Joule} = 1 \text{ kg} \cdot \text{m}^2/\text{s}^2 \]

3. **Express Ergs in Basic Units**:
- The erg can be expressed in terms of basic physical quantities:
\[ 1 \text{ erg} = 1 \text{ g} \cdot \text{cm}^2/\text{s}^2 \]

4. **Set Up the Conversion**:
- We want to find how many ergs are in 1 joule. We can set up the equation:
\[ 1 \text{ J} = n \text{ erg} \]
- Therefore, we can write:
\[ 1 \text{ kg} \cdot \text{m}^2/\text{s}^2 = n \cdot (1 \text{ g} \cdot \text{cm}^2/\text{s}^2) \]

5. **Convert Units**:
- Convert kilograms to grams:
\[ 1 \text{ kg} = 10^3 \text{ g} \]
- Convert meters to centimeters:
\[ 1 \text{ m} = 10^2 \text{ cm} \quad \Rightarrow \quad 1 \text{ m}^2 = (10^2 \text{ cm})^2 = 10^4 \text{ cm}^2 \]

6. **Substitute the Converted Units**:
- Substitute the conversions into the equation:
\[ 10^3 \text{ g} \cdot 10^4 \text{ cm}^2/\text{s}^2 = n \cdot (1 \text{ g} \cdot \text{cm}^2/\text{s}^2) \]

7. **Simplify the Equation**:
- Cancel out the common units (g, cm², and s²):
\[ 10^3 \cdot 10^4 = n \]
- Therefore:
\[ n = 10^7 \]

8. **Final Result**:
- Thus, we find that:
\[ 1 \text{ Joule} = 10^7 \text{ erg} \]

### Conclusion:
The final answer is:
\[ 1 \text{ Joule} = 10^7 \text{ erg} \]