a wooden block of density 860 kg per metre cube at zero degree celsius is floating on benzene liquid of density 900 kg per metre cube at zero degree celsius the temperature at which the block just submerge in Benzene is
To determine the temperature at which the wooden block just submerges in benzene, we need to consider the principle of buoyancy.
The buoyant force acting on an object submerged or floating in a fluid depends on the density of the fluid and the volume of the displaced fluid. For an object to float, the buoyant force must be greater than or equal to the weight of the object.
In this case, the wooden block is floating on benzene. Therefore, the weight of the block must be equal to the buoyant force acting on it.
Let's assume the volume of the wooden block is V cubic meters, and its weight is W Newtons. We can calculate the volume using the density:
Density of the wooden block = 860 kg/m^3
Weight of the wooden block (W) = Density of wood * Volume (V) * Acceleration due to gravity
The density of benzene is given as 900 kg/m^3. When the wooden block just submerges, the volume of the liquid displaced will be equal to the volume of the block. At this point, the buoyant force is equal to the weight of the block.
Buoyant force = Weight of wooden block
Density of benzene * Volume of benzene * Acceleration due to gravity = Weight of wooden block
Density of benzene * Volume * Acceleration due to gravity = Density of wood * Volume * Acceleration due to gravity
Since the acceleration due to gravity cancels out, we're left with:
Density of benzene * Volume of benzene = Density of wood * Volume
Now, we can substitute the densities:
900 kg/m^3 * Volume of benzene = 860 kg/m^3 * Volume
Rearranging the equation to solve for the volume of benzene:
Volume of benzene = (860 kg/m^3 * Volume) / 900 kg/m^3
Volume cancels out, and we're left with:
Volume of benzene = 860 / 900
Volume of benzene = 0.9556
This means that when the volume of benzene is 0.9556 times the volume of the block, the block will just submerge. The temperature at which this happens depends on the thermal expansion coefficient of benzene and the block. Given the provided information, we cannot determine the exact temperature at which the block just submerges in benzene.
So the question is what temperature does benzene have a density of 860kg/m^3?
the density of a fluid may be expressed as
rho= rhoo/(1+ Beta(tf - to)
for benzene, at to, rho is 0.8756 g/cu cm at 20 deg C, and beta is 0.00121999997646 measured at 0 degC
.860=.876/(1+0.00121999997646(Tf-0C)
solve for Tf