To analyze the relationship between the emissivity and absorptivity of two bodies, X and Y, based on their temperature versus time graphs, we need to consider the fundamental principles of thermal radiation. Emissivity (E) and absorptivity (A) are crucial properties that dictate how a body emits and absorbs thermal energy. According to Kirchhoff's law of thermal radiation, for a body in thermal equilibrium, the emissivity and absorptivity are equal at a given temperature. This means that a good emitter is also a good absorber.
Understanding Emissivity and Absorptivity
Emissivity is a measure of how effectively a surface emits thermal radiation compared to a perfect black body, which has an emissivity of 1. Absorptivity, on the other hand, indicates how well a surface absorbs radiation. For two bodies with equal surface areas, we can infer their thermal behavior from their temperature-time graphs.
Analyzing the Graphs
When examining the temperature versus time graphs for bodies X and Y, we look for key characteristics:
- Rate of Temperature Change: A steeper slope in the graph indicates a faster rate of temperature change, suggesting higher energy absorption or emission.
- Equilibrium Temperature: The temperature at which the graph levels off indicates the thermal equilibrium state of the body.
Comparing Bodies X and Y
Let’s consider the implications of the graphs. If body X reaches a higher temperature more quickly than body Y, it suggests that X has a higher absorptivity (Ax) and possibly a higher emissivity (Ex). Conversely, if Y shows a slower temperature rise, it may indicate lower absorptivity (Ay) and emissivity (Ey).
Evaluating the Options
Now, let’s evaluate the provided options:
- a) Ex > Ey & Ax > Ay: This suggests X is both a better emitter and absorber than Y.
- b) Ex < Ey & Ax > Ay: This implies Y is a better emitter, but X absorbs better.
- c) Ex > Ey & Ax < Ay: Here, X emits better but absorbs worse than Y.
- d) Ex < Ey & Ax < Ay: This indicates Y is superior in both aspects.
Conclusion Based on Graph Analysis
If body X shows a steeper temperature increase and reaches a higher equilibrium temperature than body Y, it is reasonable to conclude that:
- Ex > Ey (X emits better than Y)
- Ax > Ay (X absorbs better than Y)
Thus, the correct answer would be option a) Ex > Ey & Ax > Ay. This conclusion aligns with the principles of thermal radiation and the behavior of the bodies as observed in their temperature versus time graphs.
