A sealed container with negligible thermal cofficient of expansion contains helium (a monatomic gas). When it is heated from 300 to 600 K, the average kinetic energy of the helium atom is

Options

A. halved
B. left unchanged
C. doubled
D. become `sqrt(2)` times

Answer

To find the average kinetic energy of a helium atom when it is heated from 300 K to 600 K, we can follow these steps:

### Step 1: Understand the relationship between temperature and average kinetic energy
The average kinetic energy (KE) of a gas molecule is directly proportional to its temperature. For a monatomic ideal gas, the average kinetic energy per atom can be expressed as:

\[ KE = \frac{3}{2} k T \]

where \( k \) is the Boltzmann constant and \( T \) is the temperature in Kelvin.

### Step 2: Calculate the initial average kinetic energy
Using the initial temperature \( T_1 = 300 \, K \):

\[ KE_1 = \frac{3}{2} k T_1 = \frac{3}{2} k (300) \]

### Step 3: Calculate the final average kinetic energy
Using the final temperature \( T_2 = 600 \, K \):

\[ KE_2 = \frac{3}{2} k T_2 = \frac{3}{2} k (600) \]

### Step 4: Find the ratio of the final to initial kinetic energy
To find how the kinetic energy changes, we can take the ratio of the final kinetic energy to the initial kinetic energy:

\[ \frac{KE_2}{KE_1} = \frac{\frac{3}{2} k (600)}{\frac{3}{2} k (300)} = \frac{600}{300} = 2 \]

### Step 5: Conclusion
This means that the final average kinetic energy is twice the initial average kinetic energy:

\[ KE_2 = 2 \cdot KE_1 \]

Thus, the average kinetic energy of the helium atom after heating from 300 K to 600 K is doubled.

### Final Answer:
The average kinetic energy of the helium atom after heating will be doubled.

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