A bubble of 8 mole of helium is submerged at a certain depth in water. The temperature of water increases by `30^(@)C`. How much heat (in Joules) is added approximately to helium during expansion

Options

A. 4000 J
B. 3000 J
C. 3500 J
D. 5000 J

Explanation

To solve the problem of how much heat is added to 8 moles of helium during expansion when the temperature of water increases by 30°C, we can follow these steps:

### Step 1: Identify the process
Since the bubble is submerged at a fixed depth in water, the pressure remains constant during the expansion of the helium gas. This indicates that the process is an isobaric process.

**Hint:** Remember that in an isobaric process, the pressure remains constant.

### Step 2: Use the formula for heat transfer
For an isobaric process, the heat added (Q) can be calculated using the formula:
\[ Q = n \cdot C_p \cdot \Delta T \]
where:
- \( n \) = number of moles of gas
- \( C_p \) = molar heat capacity at constant pressure
- \( \Delta T \) = change in temperature

**Hint:** Make sure to identify the values for \( n \), \( C_p \), and \( \Delta T \).

### Step 3: Determine the values
Given:
- \( n = 8 \) moles
- \( \Delta T = 30°C \)

For helium, which is a monatomic gas, the molar heat capacity at constant pressure \( C_p \) is given by:
\[ C_p = \frac{5}{2} R \]
where \( R = 8.31 \, \text{J/(mol·K)} \).

**Hint:** Remember to convert the temperature change from Celsius to Kelvin if necessary, but since the change is the same in both scales, you can use the Celsius value directly.

### Step 4: Calculate \( C_p \)
Substituting \( R \) into the equation for \( C_p \):
\[ C_p = \frac{5}{2} \cdot 8.31 \]
\[ C_p = 20.775 \, \text{J/(mol·K)} \]

**Hint:** Calculate \( C_p \) carefully, as it is crucial for the final heat calculation.

### Step 5: Calculate the heat added
Now substitute the values into the heat transfer formula:
\[ Q = 8 \cdot 20.775 \cdot 30 \]
\[ Q = 8 \cdot 20.775 \cdot 30 = 4986 \, \text{J} \]

**Hint:** Ensure to multiply all values correctly to get the final result.

### Step 6: Round the result
The approximate value of heat added is:
\[ Q \approx 5000 \, \text{J} \]

**Hint:** Rounding off is often necessary in physics problems for simplicity.

### Final Answer
The heat added approximately to helium during expansion is **5000 Joules**.

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