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 step by step, we need to analyze the situation involving the ideal gas in the balloon and the effects of puncturing the balloon.

### 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.

**Hint:** Remember that pressure and temperature are key parameters that affect the behavior of gases.

### Step 2: Identify What Happens When the Balloon is Punctured
When the balloon is punctured, the gas inside will expand into the vacuum of the large container. Since there is no external pressure (vacuum), the gas will expand freely.

**Hint:** Consider how the absence of external pressure affects the gas expansion.

### Step 3: Apply the Ideal Gas Law
According to the ideal gas law, \( PV = nRT \). When the gas expands, the volume (V) increases. Since the gas is expanding into a vacuum, there is no work done against external pressure.

**Hint:** Recall that the ideal gas law relates pressure, volume, and temperature.

### Step 4: Consider the Internal Energy Change
For an ideal gas, the internal energy (U) depends only on temperature. The equation for internal energy change is given by:
\[ \Delta U = Q + W \]
In this case, since the gas expands into a vacuum, no heat is exchanged with the surroundings (Q = 0), and the work done (W) is also zero. Therefore, the change in internal energy is zero.

**Hint:** Remember that for an ideal gas, internal energy is a function of temperature.

### Step 5: Determine the Temperature Change
Since the internal energy change is zero and the internal energy of an ideal gas is directly related to its temperature, the temperature must remain constant during the expansion.

**Hint:** Think about how internal energy and temperature are related for an ideal gas.

### Step 6: Conclusion
Based on the analysis, we conclude that the temperature of the gas in the container remains constant after the balloon is punctured.

**Final Answer:** The temperature remains constant.

### Summary of Options:
- A) Decreases - Incorrect
- B) Increases - Incorrect
- C) Remains constant - Correct
- D) Unpredictable - Incorrect

### Final Answer: Option C - Remains constant

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