To analyze the relationship between the weights W1 and W2 of a piece of metal submerged in mercury at different temperatures, we need to consider several factors, including the effects of temperature on the metal and the properties of the fluids involved. Let's break this down step by step.
Understanding Weight in Fluids
The weight of an object submerged in a fluid is affected by the buoyant force acting on it, which is determined by the density of the fluid and the volume of the object submerged. The buoyant force can be described by Archimedes' principle, which states that the upward buoyant force is equal to the weight of the fluid displaced by the object.
Temperature Effects on Density
As temperature increases, the density of fluids generally decreases. In this case, we are dealing with mercury and a metal whose coefficient of cubical expansion is less than that of alcohol. Since the density of the metal is large compared to alcohol, we can infer that the metal will expand less than the mercury when the temperature rises from 0°C to 60°C.
Analyzing W1 and W2
At 0°C, the weight of the metal submerged in mercury is W1. At 60°C, the weight is W2. The key points to consider are:
- The volume of the metal will increase due to thermal expansion, but since the coefficient of cubical expansion of the metal is less than that of alcohol, the increase in volume will be relatively small.
- The density of mercury is significantly higher than that of alcohol, so the buoyant force acting on the metal will also change as the temperature affects the density of mercury.
Comparing the Weights
As the temperature rises, the density of mercury decreases, leading to a decrease in the buoyant force acting on the metal. Since the volume of the metal increases but at a lesser rate than the decrease in the density of mercury, the overall effect is that the buoyant force diminishes more significantly than the weight of the metal itself increases due to thermal expansion.
Thus, we can conclude that W2, the weight of the metal at 60°C, will be greater than W1, the weight at 0°C. Therefore, the relationship can be expressed as:
W2 > W1
Final Thoughts
This relationship highlights the interplay between temperature, density, and buoyancy in fluids. The specific properties of the materials involved—such as the coefficients of expansion and densities—play a crucial role in determining how the weight of the submerged object changes with temperature. Understanding these principles can help in various applications, from engineering to materials science.
