The slope of `'P'` v/s `"T"` plot at constant volume for a fixed amount of an ideal gas aus `0.01 atm//K`. Then what will be the value of pressure of gas `("In atm")` at `300 K` temperature ?

Explanation

To solve the problem, we will use the relationship between pressure (P) and temperature (T) for an ideal gas at constant volume. The slope of the P vs. T plot is given, and we can use this information to find the pressure at a specific temperature.

### Step-by-step Solution:

1. **Understand the relationship**: For an ideal gas, the equation of state is given by:
\[ PV = nRT \]
Rearranging this for pressure (P), we get:
\[ P = \frac{nR}{V} \cdot T \]
Here, \( \frac{nR}{V} \) is a constant at constant volume for a fixed amount of gas.

2. **Identify the slope**: The slope of the P vs. T plot at constant volume is given as:
\[ \text{slope} = \frac{P}{T} \]
According to the problem, this slope is \( 0.01 \, \text{atm/K} \).

3. **Set up the equation**: We can express the pressure in terms of the slope and temperature:
\[ P = \text{slope} \times T \]

4. **Substitute the values**: We need to find the pressure at \( T = 300 \, \text{K} \):
\[ P = 0.01 \, \text{atm/K} \times 300 \, \text{K} \]

5. **Calculate the pressure**:
\[ P = 0.01 \times 300 = 3 \, \text{atm} \]

### Final Answer:
The pressure of the gas at 300 K is \( 3 \, \text{atm} \).

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