When the temperature of an ideal gas is increased from `27^@C `to `927^@C`, the kinetic energy will be

Options

A. same
B. eight times
C. four times
D. twice.

Explanation

To find the change in kinetic energy of an ideal gas when its temperature is increased from 27°C to 927°C, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Temperatures from Celsius to Kelvin**:
- The formula to convert Celsius to Kelvin is:
\[ T(K) = T(°C) + 273 \]
- For the initial temperature \( T_1 \):
\[ T_1 = 27°C + 273 = 300 K \]
- For the final temperature \( T_2 \):
\[ T_2 = 927°C + 273 = 1200 K \]

2. **Use the Kinetic Energy Formula**:
- The kinetic energy (KE) of an ideal gas is given by:
\[ KE = \frac{3}{2} RT \]
- Where \( R \) is the universal gas constant and \( T \) is the temperature in Kelvin.

3. **Calculate Initial Kinetic Energy**:
- For the initial temperature \( T_1 = 300 K \):
\[ KE_1 = \frac{3}{2} R (300) \]

4. **Calculate Final Kinetic Energy**:
- For the final temperature \( T_2 = 1200 K \):
\[ KE_2 = \frac{3}{2} R (1200) \]

5. **Determine the Change in Kinetic Energy**:
- The change in kinetic energy (\( \Delta KE \)) can be calculated as:
\[ \Delta KE = KE_2 - KE_1 \]
- Substituting the values:
\[ \Delta KE = \left(\frac{3}{2} R (1200)\right) - \left(\frac{3}{2} R (300)\right) \]
- Factor out \( \frac{3}{2} R \):
\[ \Delta KE = \frac{3}{2} R (1200 - 300) = \frac{3}{2} R (900) \]

6. **Calculate the Ratio of Kinetic Energies**:
- To find how many times the final kinetic energy is compared to the initial kinetic energy:
\[ \frac{KE_2}{KE_1} = \frac{\frac{3}{2} R (1200)}{\frac{3}{2} R (300)} = \frac{1200}{300} = 4 \]

### Conclusion:
The final kinetic energy is **4 times** the initial kinetic energy when the temperature of the ideal gas is increased from 27°C to 927°C.