Which one of the following graphs shows the rate at which heat is emitted from a hot body as a function of its Kelvin temperature T' ?

Options

A.
B.
C.
D.

Answer

To determine which graph shows the rate at which heat is emitted from a hot body as a function of its Kelvin temperature \( T' \), we can follow these steps:

### Step 1: Understand the relationship
The rate of heat emission from a hot body is described by Stefan-Boltzmann Law, which states that the rate of heat emission \( R \) is proportional to the fourth power of the absolute temperature \( T \) (in Kelvin). Mathematically, this can be expressed as:
\[ R \propto T^4 \]

### Step 2: Analyze the relationship
Since \( R \) is proportional to \( T^4 \), we can express this as:
\[ R = k T^4 \]
where \( k \) is a constant. This indicates that as the temperature increases, the rate of heat emission increases rapidly.

### Step 3: Identify the graph shape
The graph of \( R \) versus \( T' \) (where \( T' \) is the temperature in Kelvin) will not be a straight line because it is a fourth-degree polynomial relationship. Instead, it will be a curve that starts from the origin and rises steeply as \( T' \) increases.

### Step 4: Review the options
Given the description of the graphs provided in the question, we need to identify which graph represents a curve that starts at the origin and rises steeply, indicating the fourth power relationship.

### Step 5: Select the correct graph
Upon reviewing the options, the graph that shows an upward curve starting from the origin is the one that represents the relationship \( R \propto T^4 \).

### Conclusion
Therefore, the correct answer is **Option 4**, as it depicts the rate of heat emission as a function of Kelvin temperature \( T' \) with the appropriate curve shape.

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