Volume of the air that will be expelled from a vessel of `300 cm^(3)` when it is heated from `27^(@)C` to `37^(@) C` at the same pressure will be

Options

A. `"310 cm"^(3)`
B. `"290 cm"^(3)`
C. `"10 cm"^(3)`
D. `"37 cm"^(3)`

Explanation

To solve the problem of finding the volume of air expelled from a vessel when heated from 27°C to 37°C at constant pressure, we can use the ideal gas law and the concept of direct proportionality between volume and temperature.

### Step-by-Step Solution:

1. **Identify Initial Conditions:**
- Initial volume (V1) = 300 cm³
- Initial temperature (T1) = 27°C

2. **Convert Temperatures to Kelvin:**
- To convert Celsius to Kelvin, use the formula:
\[ T(K) = T(°C) + 273 \]
- For T1:
\[ T1 = 27 + 273 = 300 \, K \]
- For T2 (final temperature):
\[ T2 = 37 + 273 = 310 \, K \]

3. **Use the Ideal Gas Law Relationship:**
- Since pressure (P) and the number of moles (n) are constant, we can use the relationship:
\[ \frac{V2}{V1} = \frac{T2}{T1} \]
- Rearranging gives:
\[ V2 = V1 \times \frac{T2}{T1} \]

4. **Substitute Known Values:**
- Substitute V1, T1, and T2 into the equation:
\[ V2 = 300 \, cm³ \times \frac{310 \, K}{300 \, K} \]
- Simplifying:
\[ V2 = 300 \, cm³ \times 1.0333 = 310 \, cm³ \]

5. **Calculate Volume of Air Expelled:**
- The volume of air expelled (V_exp) is the difference between the final volume (V2) and the initial volume (V1):
\[ V_{exp} = V2 - V1 \]
- Substituting the values:
\[ V_{exp} = 310 \, cm³ - 300 \, cm³ = 10 \, cm³ \]

### Final Answer:
The volume of air expelled from the vessel is **10 cm³**.

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