An ideal gas filled at pressure `2 atm` and temp of `300 K`, in a balloon is kept in vaccum with in a large container wall of balloon is punchtured then container temperature :

Options

A. Decreases
B. Increases
C. Remain constant
D. Unpredictable

Answer

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

### Step 1: Understand the Initial Conditions
The ideal gas in the balloon is at a pressure of 2 atm and a temperature of 300 K. It is important to note that these conditions are stable before the balloon is punctured.

**Hint:** Identify the initial state of the gas, including pressure and temperature.

### Step 2: Recognize the Environment
The balloon is kept in a vacuum within a large container. This means that there is no external pressure acting on the gas in the balloon once it is punctured.

**Hint:** Consider how the vacuum affects the behavior of the gas when the balloon is punctured.

### Step 3: Puncturing the Balloon
When the wall of the balloon is punctured, the gas inside will expand into the vacuum of the container. Since there is no opposing pressure from the outside, the gas will fill the available volume of the container.

**Hint:** Think about what happens to the gas when it is allowed to expand freely into a vacuum.

### Step 4: Apply Boyle's Law
According to Boyle's Law, for a given amount of gas at constant temperature, the pressure and volume are inversely related (PV = constant). In this case, as the volume increases (due to expansion), the pressure must decrease.

**Hint:** Recall that Boyle's Law applies when temperature remains constant during the process.

### Step 5: Determine the Temperature Change
Since the gas expands into a vacuum and there is no heat exchange with the surroundings (the container is in a vacuum), the process can be considered adiabatic for the gas. However, because we are not adding or removing heat, and because the gas is ideal, the temperature of the gas remains constant during the expansion.

**Hint:** Consider the implications of an adiabatic process and the characteristics of an ideal gas.

### Conclusion
The temperature of the gas after the balloon is punctured remains at 300 K, as there is no heat exchange and the process does not involve any work done on or by the gas.

**Final Answer:** The temperature of the container after the balloon is punctured is 300 K.

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