A bolloon blown up has a volume of 300 mL at `27%` C. The balloon is distended to `(5)/(6)` of its maximum stretching capacity. The maximum temperature above which it will burst is

Options

A. `77^@C`
B. `67^@C`
C. `57^@C`
D. `87^@C`

Explanation

To solve the problem of determining the maximum temperature above which a balloon will burst, we can follow these steps:

### Step 1: Understand the given values
- The initial volume of the balloon (V1) = 300 mL
- The initial temperature (T1) = 27°C
- The balloon is distended to (5/6) of its maximum capacity.

### Step 2: Convert the initial temperature to Kelvin
To use the gas laws, we need to convert the temperature from Celsius to Kelvin.
\[ T1 = 27°C + 273 = 300 \, K \]

### Step 3: Calculate the maximum volume of the balloon
The balloon is distended to (5/6) of its maximum capacity. Let’s denote the maximum volume as V_max. We can set up the equation:
\[ \frac{5}{6} V_{max} = 300 \, mL \]
To find V_max, we rearrange the equation:
\[ V_{max} = 300 \times \frac{6}{5} = 360 \, mL \]

### Step 4: Use the combined gas law
According to the combined gas law, we have:
\[ \frac{V1}{T1} = \frac{V2}{T2} \]
Where:
- V1 = 300 mL (initial volume)
- T1 = 300 K (initial temperature)
- V2 = 360 mL (maximum volume)
- T2 = ? (maximum temperature in Kelvin)

### Step 5: Substitute the known values into the equation
Substituting the known values into the equation:
\[ \frac{300}{300} = \frac{360}{T2} \]

### Step 6: Solve for T2
Cross-multiplying gives:
\[ 300 \cdot 360 = 300 \cdot T2 \]
\[ T2 = \frac{300 \cdot 360}{300} = 360 \, K \]

### Step 7: Convert T2 back to Celsius
To find the maximum temperature in Celsius:
\[ T2 = 360 \, K - 273 = 87°C \]

### Conclusion
The maximum temperature above which the balloon will burst is **87°C**.

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