Describe how can you determine the volume of the coil by using a measuring cylinder
Answers
Density Determinations and Various Methods to Measure Volume
GOAL AND OVERVIEW
This lab provides an introduction to the concept and applications of density measurements. The densities of brass and aluminum will be calculated from mass and volume measurements. To illustrate the effects of precision on data, volumes will be determined by three different methods: geometrically (measuring lengths); water displacement; and pycnometry. The composition of a mixed brass-aluminum cylinder and the volume of empty space within a hollow cylinder will also be found.
Objectives of the Data Analysis
•
Determine volume by three different methods
•
Use measured volumes and masses to calculate densities
•
Use the relationship between mass, volume, and density to find desired unknown quantities
•
Evaluate results using error analysis
SUGGESTED REVIEW AND EXTERNAL READING
•
Data analysis introduction, textbook information on density
INTRODUCTION
The density, ρ, of an object is defined as the ratio of its mass to its volume. Density can be useful in identifying substances. It is also a convenient property because it provides a link (or conversion factor) between the mass and the volume of a substance.
( 1 )
ρ = m/V
Mass and volume are extensive (or extrinsic) properties of matter - they depend on amount. Density, an intensive (or intrinsic) property, is a kind of "heaviness" factor. In macroscopic terms, density reflects how much mass is packed into a given three-dimensional space. Typically, densities are reported g/ml or g/cm3 (which are equivalent because 1ml ≡ 1cm3). Experimentally, mass and volume measurements are required to calculate density.
Masses are measured on electronic balances. Pan balances, which are accurate to ±0.01 g, are used for quick measurements where greater precision is not required. Analytical balances (accurate to ±0.0001 g) are used for more precise measurements.
Volume is an amount of space, in three dimensions, that a sample of matter occupies. The number and the phase of the molecules in the sample primarily determine the volume of a substance. Volume will be measured in many ways in this course, but the units are usually milliliters (mL) or cubic centimeters (cm3). Methods for determining or delivering precise volumes include volumetric pipets and pycnometers; less precise methods include burets, graduated cylinders, and graduated pipets.
In this experiment, you will measure masses and volumes to determine density. Four different metal cylinders are investigated.
In parts 1-3, three different methods are used to find volume of two solid metal cylinders (Al and brass). Each method has its own degree of precision.
(i)
volume by geometry
(ii)
volume by water displacement
(iii)
volume by pycnometry (mass-based)
In parts 4-5, one method for volume determination is used to find:
(i)
the volume of a void inside a hollow cylinder; and,
(ii)
the percent composition of a mixed-metal cylinder.
Volume by geometry
A cylinder is a standard geometric form. In this case, you can measure the dimensions of the cylinder and apply the formula to calculate its volume.
( 2a )
V = π
d
2
2
l =
π
4
d 2 l where d = diameter and l = length.
Figure 1
Figure 1
Density would be calculated in one step to minimize rounding errors:
( 2b )
ρ =
m
V
=
4m
πd 2 l
The uncertainty in the volume must be determined by error propagation. Mass, length, and diameter measurements contribute to the overall uncertainty.
( 2c )
σ ρ = ± ρ
σ d
d
+
σ d
d
+
σ l
l
+
σ m
m
Volume by water displacement
For less defined shapes, volume can be determined by water displacement. Volumes of liquids such as water can be readily measured in a graduated cylinder.
To use the water displacement method, an object (in this case, a small metal cylinder) is inserted into a graduated cylinder partially filled with water. The object's volume occupies space, displacing liquid and raising the water level. The difference between the two volumes, before and after the object was inserted, is the object's volume.
Figure 2
Figure 2
( 3a )
Vcyl = Vfinal − Vinitial = Vwater + cyl − Vwater
The uncertainty of the volume is based on the two volume readings.
( 3b )
σ Vcyl = σ Vfinal + σ Vinitial
The density is calculated using m/V. There is not a straightforward way to find density in one step (as with geometry).
The uncertainty in the density would be given by:
( 3c )
σ ρ = ± ρ
σ V
V
+
σ m
m