If temperature of IBB is decrease by T to T/2 than worked out percentage loss in emissive rate

Explanation

To solve the problem of finding the percentage loss in emissive rate when the temperature decreases from \( T \) to \( \frac{T}{2} \), we can follow these steps:

### Step 1: Understand the relationship between emissive power and temperature
According to Stefan-Boltzmann Law, the emissive power \( E \) of a body is proportional to the fourth power of its absolute temperature \( T \):
\[ E \propto T^4 \]
This means that if we know the temperature, we can find the emissive power.

### Step 2: Calculate the initial emissive power
Let the initial temperature be \( T \). The initial emissive power \( E \) can be expressed as:
\[ E = k T^4 \]
where \( k \) is a proportionality constant.

### Step 3: Calculate the emissive power at the new temperature
When the temperature decreases to \( \frac{T}{2} \), the new emissive power \( E' \) can be expressed as:
\[ E' = k \left(\frac{T}{2}\right)^4 \]
Calculating this gives:
\[ E' = k \frac{T^4}{16} \]

### Step 4: Find the percentage loss in emissive power
The percentage loss in emissive power can be calculated using the formula:
\[ \text{Percentage Loss} = \left( \frac{E - E'}{E} \right) \times 100 \]
Substituting the values of \( E \) and \( E' \):
\[ \text{Percentage Loss} = \left( \frac{E - \frac{E}{16}}{E} \right) \times 100 \]
This simplifies to:
\[ \text{Percentage Loss} = \left( \frac{1 - \frac{1}{16}}{1} \right) \times 100 \]
Calculating this gives:
\[ \text{Percentage Loss} = \left( \frac{15}{16} \right) \times 100 = 93.75\% \]

### Final Answer
Thus, the percentage loss in emissive rate when the temperature decreases from \( T \) to \( \frac{T}{2} \) is approximately \( 93.75\% \).

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