An iron cube floats in a bowl of liquid mercury at 0 C.

a) If the temperature is raised to 28 C, will the cube float higher or lower in the mercury?
b)By what percent will the fraction of volume submerged change?

Thanks

To understand the behavior of the iron cube in the liquid mercury, we need to consider the density and thermal expansion properties of both substances.

a) If the temperature is raised from 0°C to 28°C, both the iron cube and the liquid mercury will undergo thermal expansion. However, the rate of expansion for mercury is significantly larger than that of iron. As a result, the volume increase in mercury will be greater compared to the increase in the iron cube's volume.

Since the density of an object determines whether it floats or sinks in a fluid, the change in volume will affect the buoyancy. If the volume of the mercury increases more than the volume of the iron cube, the cube will displace less liquid and consequently float higher in the mercury. Therefore, the cube will float higher when the temperature is raised to 28°C.

b) To determine the percent change in the fraction of volume submerged, we can use the concept of buoyancy. The fraction of the volume of the cube submerged can be calculated as the ratio of the volume of the cube submerged in mercury to the total volume of the cube.

Let's assume that initially, a fraction "x" of the cube's volume is submerged at 0°C. When the temperature is raised to 28°C, the fraction of volume submerged will change due to the combined effects of thermal expansion of both substances.

Using the formula for thermal expansion ∆L = (α * L_initial * ∆T), where ∆L is the change in length, α is the coefficient of linear expansion, L_initial is the initial length, and ∆T is the change in temperature.

Since we are interested in the change in volume, we can use the formula ∆V = β * V_initial * ∆T, where ∆V is the change in volume, β is the coefficient of volume expansion, and V_initial is the initial volume.

The change in volume of mercury (∆V_mercury) and the change in volume of iron (∆V_iron) can be calculated using their respective coefficients of volume expansion (β_mercury and β_iron).

The fraction of volume submerged can be expressed as:

Fraction submerged = (V_initial - ∆V_iron) / V_initial

To find the percent change, we can use the formula:

Percent Change = [(Fraction submerged at 28°C - Fraction submerged at 0°C) / Fraction submerged at 0°C] * 100

By plugging in the values for the coefficients of volume expansion of mercury and iron, as well as the change in temperature, we can calculate the percent change in the fraction of volume submerged.

It's worth mentioning that the numerical values for the coefficients of volume expansion for mercury and iron may vary depending on the specific type or grade of the material used.

a) When the temperature is raised from 0°C to 28°C, the liquid mercury will expand due to thermal expansion. However, the iron cube will also expand, but to a lesser extent than the mercury.

The expansion of the mercury will result in an increase in its density, while the expansion of the iron cube will result in a decrease in its density.

Since the density of the iron cube decreases more than the density of the mercury increases, the cube will float lower in the mercury when the temperature is raised to 28°C.

b) To calculate the change in the fraction of volume submerged, we need to compare the initial volume submerged with the new volume submerged.

Let's assume that initially, a fraction x of the iron cube's volume is submerged.

At the higher temperature of 28°C, the iron cube will expand and its volume will increase, leading to a decrease in the fraction of volume submerged.

The change in the fraction of volume submerged can be calculated using the equation:

Change in fraction = (Initial volume submerged - New volume submerged)/Initial volume submerged

Now, since the iron cube is still floating, the weight of the iron cube is equal to the buoyant force acting on it.

The buoyant force is given by the equation:

Buoyant force = Weight of displaced liquid

Therefore, the initial volume submerged can be determined by equating the weight of the iron cube to the buoyant force at 0°C.

However, without the dimensions or mass of the iron cube or the specific dimensions of the bowl of liquid mercury provided, it is not possible to provide an exact calculation for the change in the fraction of volume submerged.

Please provide the necessary details if you want a specific calculation.

You need the density of iron, mercury, at each temperature, or have the coefficent of volume expansion and then figure the density at the second temp.