A container of volume `1m^3` is divided into two equal parts by a partition. One part has an ideal gas at 300K and the other part is vacuum. The whole system is thermally isolated from the surroundings. When the partition is removed, the gas expands to occupy the whole volume. Its temperature will now be .......

Explanation

To solve the problem, we need to analyze the situation step by step.

### Step 1: Understand the Initial Conditions
We have a container of volume 1 m³ divided into two equal parts (0.5 m³ each). One part contains an ideal gas at a temperature of 300 K, and the other part is a vacuum.

**Hint:** Identify the properties of the gas and the vacuum before the partition is removed.

### Step 2: Remove the Partition
When the partition is removed, the ideal gas expands to fill the entire volume of 1 m³. Since the other part is a vacuum, there is no opposing pressure.

**Hint:** Consider what happens to the gas when it expands into a vacuum.

### Step 3: Analyze the Work Done
In this scenario, the gas expands into a vacuum. According to the principles of thermodynamics, when a gas expands into a vacuum, no work is done by the gas because there is no external pressure to work against.

**Hint:** Recall the definition of work done in thermodynamics and how it applies to expansion against vacuum.

### Step 4: Consider the Heat Exchange
The system is thermally isolated, meaning that no heat can enter or leave the system. Since the gas expands into a vacuum and there is no heat exchange, the heat (Q) is also zero.

**Hint:** Remember the concept of adiabatic processes where no heat is exchanged.

### Step 5: Apply the First Law of Thermodynamics
The first law of thermodynamics states that the change in internal energy (∆U) of a system is equal to the heat added to the system (Q) minus the work done by the system (W):
\[ \Delta U = Q - W \]

In our case:
- \( Q = 0 \) (no heat exchange)
- \( W = 0 \) (no work done)

Thus, we have:
\[ \Delta U = 0 - 0 = 0 \]

**Hint:** Use the first law of thermodynamics to relate internal energy, heat, and work.

### Step 6: Determine the Temperature Change
Since the internal energy of an ideal gas is directly related to its temperature, if there is no change in internal energy, there will be no change in temperature. Therefore, the temperature of the gas remains at 300 K after the expansion.

**Hint:** Recall the relationship between internal energy and temperature for an ideal gas.

### Final Answer
The temperature of the gas after it expands to occupy the whole volume will be **300 K**.