A gas is filled in a container of volume V. at constant pressure and `27^@ C` temperature. Find out the amount of gas that will escape out of the container if temperature rises to `37^@ C`.

Answer

To solve the problem of how much gas escapes from a container when the temperature rises from 27°C to 37°C at constant pressure, we can use the ideal gas law and the relationship between volume and temperature.

### Step-by-Step Solution:

1. **Convert Temperatures to Kelvin:**
- The initial temperature \( T_1 = 27^\circ C = 27 + 273 = 300 \, K \)
- The final temperature \( T_2 = 37^\circ C = 37 + 273 = 310 \, K \)

2. **Use the Ideal Gas Law:**
- According to the ideal gas law, at constant pressure, the volume of a gas is directly proportional to its temperature (in Kelvin).
- Therefore, we can write the relationship as:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
- Where \( V_1 \) is the initial volume and \( V_2 \) is the final volume.

3. **Substitute Known Values:**
- We know \( V_1 = V \), \( T_1 = 300 \, K \), and \( T_2 = 310 \, K \).
- Substitute these values into the equation:
\[ \frac{V}{300} = \frac{V_2}{310} \]

4. **Solve for \( V_2 \):**
- Cross-multiply to find \( V_2 \):
\[ V_2 = \frac{310}{300} \times V = \frac{31}{30} V \]

5. **Calculate the Change in Volume:**
- The change in volume \( \Delta V \) is given by:
\[ \Delta V = V_2 - V_1 = \frac{31}{30} V - V = \left(\frac{31}{30} - 1\right)V = \left(\frac{31 - 30}{30}\right)V = \frac{1}{30} V \]

6. **Determine the Amount of Gas Escaped:**
- The amount of gas that escapes is proportional to the change in volume. Therefore, the amount of gas that escapes is:
\[ \Delta V = \frac{1}{30} V \]

### Final Answer:
The amount of gas that will escape out of the container is \( \frac{1}{30} V \).