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 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 an 8 mole bubble of helium during expansion when the temperature of the surrounding water increases by 30°C, we can follow these steps:

### Step 1: Identify the type of process
The problem states that the bubble is submerged in water and the temperature of the water increases, which implies that the process can be considered an isobaric process (constant pressure).

### Step 2: Use the formula for heat transfer
In 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 the gas (helium in this case)
- \( C_p \) = specific heat capacity at constant pressure
- \( \Delta T \) = change in temperature

### Step 3: Determine the values
- Given \( n = 8 \) moles (for helium).
- The change in temperature \( \Delta T = 30°C \).
- For a monoatomic gas like helium, the specific heat capacity at constant pressure \( C_p \) is given by:
\[ C_p = \frac{5}{2} R \]
where \( R \) is the universal gas constant, approximately \( 8.31 \, \text{J/(mol·K)} \).

### Step 4: Calculate \( C_p \)
Substituting the value of \( R \):
\[ C_p = \frac{5}{2} \times 8.31 \approx 20.78 \, \text{J/(mol·K)} \]

### Step 5: Substitute values into the heat transfer formula
Now substituting \( n \), \( C_p \), and \( \Delta T \) into the heat transfer formula:
\[ Q = 8 \cdot 20.78 \cdot 30 \]

### Step 6: Perform the calculation
Calculating \( Q \):
\[ Q = 8 \cdot 20.78 \cdot 30 = 4986.4 \, \text{J} \]

### Step 7: Round the answer
Approximately, we can round this to:
\[ Q \approx 5000 \, \text{J} \]

### Final Answer
The amount of heat added approximately to helium during expansion is **5000 J**.

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