A perfect gas at `27^(@)C` is heated at constant pressure so as to triple its volume. The tmemperature of th gas will be

Options

A. `84^(@)C`
B. `900^(@)C`
C. `627^(@)C`
D. `450^(@)C`

Explanation

To solve the problem, we will use the ideal gas law and the relationship between volume and temperature at constant pressure.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Initial temperature \( T_i = 27^\circ C \)
- The gas is heated at constant pressure.
- The volume triples, so \( V_f = 3V_i \).

2. **Convert Initial Temperature to Kelvin**:
- The temperature in Kelvin is given by the formula:
\[ T(K) = T(°C) + 273 \]
- Thus,
\[ T_i = 27 + 273 = 300 \, K \]

3. **Use the Relationship Between Volume and Temperature**:
- At constant pressure, the volume of a gas is directly proportional to its temperature (in Kelvin). This can be expressed as:
\[ \frac{V_i}{V_f} = \frac{T_i}{T_f} \]
- Since \( V_f = 3V_i \), we can rewrite this as:
\[ \frac{V_i}{3V_i} = \frac{T_i}{T_f} \]
- Simplifying gives:
\[ \frac{1}{3} = \frac{T_i}{T_f} \]

4. **Rearranging the Equation**:
- Rearranging the equation to solve for \( T_f \):
\[ T_f = 3T_i \]

5. **Substituting the Initial Temperature**:
- Now substitute \( T_i = 300 \, K \):
\[ T_f = 3 \times 300 = 900 \, K \]

6. **Convert Final Temperature Back to Celsius**:
- To convert \( T_f \) back to Celsius:
\[ T(°C) = T(K) - 273 \]
- Thus,
\[ T_f = 900 - 273 = 627^\circ C \]

### Final Answer:
The temperature of the gas after heating will be \( 627^\circ C \).

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