Work done during isothermal expansion of one mole of an ideal gas form 10atm to 1atm at 300K is (Gas constant=`2`)

Explanation

To solve the problem of calculating the work done during the isothermal expansion of one mole of an ideal gas from 10 atm to 1 atm at 300 K, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Number of moles, \( n = 1 \) mole
- Initial pressure, \( P_1 = 10 \) atm
- Final pressure, \( P_2 = 1 \) atm
- Temperature, \( T = 300 \) K
- Gas constant, \( R = 2 \) (in appropriate units)

2. **Use the Formula for Work Done**:
The work done during isothermal expansion can be calculated using the formula:
\[ W = -nRT \log\left(\frac{P_1}{P_2}\right) \]
Alternatively, it can also be expressed in terms of volumes:
\[ W = -nRT \log\left(\frac{V_2}{V_1}\right) \]
However, since we have pressures, we will use the first formula.

3. **Substitute the Values into the Formula**:
Substitute the known values into the formula:
\[ W = -1 \times 2 \times 300 \times \log\left(\frac{10}{1}\right) \]

4. **Calculate the Logarithm**:
Since \( \log(10) = 1 \):
\[ W = -1 \times 2 \times 300 \times 1 \]

5. **Perform the Multiplication**:
\[ W = -600 \text{ (in appropriate units)} \]

6. **Convert Units if Necessary**:
If the work is required in calories, we need to convert the result. Assuming the gas constant is given in calories, we can directly state:
\[ W = -600 \text{ calories} \]

### Final Answer:
The work done during the isothermal expansion of one mole of an ideal gas from 10 atm to 1 atm at 300 K is:
\[ W = -600 \text{ calories} \]