by Nick Connor

What is Volume – Physics. Volume is a basic physical quantity. Volume is a derived quantity and it expresses the three dimensional extent of an object. Thermal Engineering

## What is Volume

**Volume** is a basic **physical quantity**. **Volume** is a derived quantity and it expresses the t**hree dimensional extent** of an **object**. Volume is often quantified numerically using the SI derived unit, the **cubic metre**. For example, the volume inside a **sphere** (that is the volume of a ball) is derived to be** V = 4/3πr ^{3}**, where r is the radius of the sphere. As another example, volume of a cube is equal to side times side times side. Since each side of a square is the same, it can simply be the length of one side

**cubed**.

If a square has one side of 3metres, the volume would be 3metrestimes 3metrestimes 3metres, or 27cubic metres.

Formulas for Calculation of Different Volumes

**Volume formulas** for some common three-dimensional objects:

## What is Specific Volume

**Specific volume** is an** intensive variable**, whereas volume is an extensive variable. The standard unit for specific volume in the SI system is cubic meters per kilogram (m^{3}/kg). The standard unit in the English system is cubic feet per pound mass (ft^{3}/lbm).

The density (ρ) of a substance is the reciprocal of its** specific volume** (ν).

**ρ = m/V = 1/ρ**

**Density** is defined as the **mass per unit volume**. It is also an **intensive property**, which is mathematically defined as mass divided by volume:

**ρ = m/V**

Materials with Lowest Specific Volume - Densest Materials on the Earth

Since **nucleons** (**protons** and **neutrons**) make up most of the mass of ordinary atoms, the density of normal matter tends to be limited by how closely we can pack these nucleons and depends on the internal atomic structure of a substance. The **densest material** found on earth is the **metal osmium**, but its density pales by comparison to the densities of exotic astronomical objects such as white** dwarf stars** and **neutron stars**.

**List of densest materials:**

- Osmium – 22.6 x 10
^{3}kg/m^{3} - Iridium – 22.4 x 10
^{3}kg/m^{3} - Platinum – 21.5 x 10
^{3}kg/m^{3} - Rhenium – 21.0 x 10
^{3}kg/m^{3} - Plutonium – 19.8 x 10
^{3}kg/m^{3} - Gold – 19.3 x 10
^{3}kg/m^{3} - Tungsten – 19.3 x 10
^{3}kg/m^{3} - Uranium – 18.8 x 10
^{3}kg/m^{3} - Tantalum – 16.6 x 10
^{3}kg/m^{3} - Mercury – 13.6 x 10
^{3}kg/m^{3} - Rhodium – 12.4 x 10
^{3}kg/m^{3} - Thorium – 11.7 x 10
^{3}kg/m^{3} - Lead – 11.3 x 10
^{3}kg/m^{3} - Silver – 10.5 x 10
^{3}kg/m^{3}

It must be noted, plutonium is a man-made isotope and is created from uranium in nuclear reactors. But, In fact, scientists have found trace amounts of naturally-occurring plutonium.

If we include man made elements, the densest so far is** Hassium**. **Hassium** is a chemical element with symbol **Hs** and atomic number 108. It is a synthetic element (first synthesised at Hasse in Germany) and radioactive. The most stable known isotope, ** ^{269}Hs**, has a half-life of approximately 9.7 seconds. It has an estimated density of

**40.7 x 10**. The density of Hassium results from its

^{3}kg/m^{3}**high atomic weight**and from the significant decrease in

**ionic radii**of the elements in the lanthanide series, known as

**lanthanide and actinide contraction**.

The density of Hassium is followed by **Meitnerium** (element 109, named after the physicist Lise Meitner), which has an estimated density of** 37.4 x 10 ^{3} kg/m^{3}**.

Changes in Specific Volume

In general, **density** and thus the **specific volume**can be **changed** by changing either the **pressure** or the **temperature**. Increasing the **pressure always increases** the **density** of a material. The effect of pressure on the densities of **liquids** and **solids** is very very small. On the other hand, the density of gases is strongly affected by pressure. This is expressed by **compressibility**. **Compressibility** is a measure of the relative volume change of a fluid or solid as a response to a pressure change.

The **effect of temperature** on the densities of liquids and solids is also very important. Most substances **expand when heated** and **contract when cooled**. However, the amount of expansion or contraction varies, depending on the material. This phenomenon is known as **thermal expansion**. The change in volume of a material which undergoes a temperature change is given by following relation:

where ∆T is the change in temperature, V is the original volume, ∆V is the change in volume, and **α _{V}** is the

**coefficient of volume expansion**.

It must be noted, there are exceptions from this rule. For example, **water** differs from most liquids in that it becomes **less dense as it freezes**. It has a maximum of density at 3.98 °C (1000 kg/m^{3}), whereas the density of ice is 917 kg/m^{3}. It differs by about 9% and therefore** ice floats** on liquid water

## Volume of an Atom and Nucleus

**The atom** consist of a small but massive **nucleus** surrounded by a cloud of rapidly moving **electrons**. The nucleus is composed of **protons and ****neutrons**. Typical nuclear radii are of the order 10^{−14} m. Assuming spherical shape, nuclear radii can be calculated according to following formula:

r = r_{0} . A^{1/3}

where r_{0} = 1.2 x 10^{-15 }m = 1.2 fm

If we use this approximation, we therefore expect the volume of the nucleus to be of the order of 4/3πr^{3} or 7,23 ×10^{−45 }m^{3} for hydrogen nuclei or 1721×10^{−45} m^{3} for ^{238}U nuclei. These are volumes of nuclei and atomic nuclei (protons and neutrons) contains of about **99.95%** of mass of atom.

## Is an atom an empty space?

**The volume of an atom** is about **15 orders of magnitude** **larger** than the volume of a nucleus. For **uranium atom**, the **Van der Waals radius** is about **186 pm = 1.86 ×10 ^{−10} m**. The Van der Waals radius, r

_{w}, of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. Assuming spherical shape, the uranium atom have volume of about

**26.9 ×10**. But this “huge” space is occupied primarilyby electrons, because the

^{−30}m^{3}**nucleus**occupies only about

**1721×10**of space. These electrons together weigh only a fraction (let say 0.05%) of entire atom.

^{−45}m^{3}It may seem, that the space and in fact the matter is **empty**, **but it is not**. Due to the **quantum nature of electrons**, the electrons are not point particles, they are smeared out over the whole atom. The classical description cannot be used to describe things on the atomic scale. On the atomic scale, physicists have found that quantum mechanics describes things very well on that scale. Particle locations in quantum mechanics are not at an exact position, they are described by a **probability density function**. Therefore the space in an atom (between electrons and an atomic nucleus) is not empty, but it is filled by a probability density function of electrons (usually known as “**electron cloud**“).

## Volume of Coolant in Reactor Coolant System

In typical modern **pressurized water reactors** (PWRs), the **Reactor Coolant System** (RCS), shown in the figure, consists of:

- the
**reactor vessel**, which contains the nuclear fuel - four parallel heat transfer
**loops**connected to a reactor vessel. - each loop contains a
**main coolant pump**and a**steam generator**. - the system includes a
**pressurizer**and its auxiliary systems

All RCS components are located inside the containment building.

At normal operation, there is a compressed liquid water inside the reactor vessel, loops and steam generators. The pressure is maintained at approximately **16MPa**. At this pressure water boils at approximately **350°C** (662°F). Inlet temperature of the water is about** 290°C** (554°F). The water (coolant) is heated in the reactor core to approximately** 325°C** (617°F) as the water flows through the core. As it can be seen, the reactor containsapproximately 25°C subcooled coolant (distance from the saturation).This high pressure is maintained by the pressurizer, a separate vessel that is connected to the primary circuit (hot leg) and partially filled with water (partially with saturated steam) which is heated to the saturation temperature (boiling point) for the desired pressure by submerged **electrical heaters**. Temperature in the pressurizer can be maintained at 350 °C. At normal conditions, about **60%** of volume of pressurizer occupies the **compressed water** and about **40%** of volume occupies the **saturated steam**.

Volumes of typical PWR are in the following table.

**It is an illustrative example, following data do not correspond to any reactor design.**

It must be noted the **volume of coolant** significantly **changes** with the **temperature** of the coolant. The** total mass** of the coolant remains always the same, a change in water volume is not a change in water inventory. The reactor coolant volume changes with temperature because of **changes in density**. Most substances **expand w****hen heated** and **contract when cooled**. However, the amount of expansion or contraction varies, depending on the material. This phenomenon is known as **thermal expansion**. The change in volume of a material which undergoes a temperature change is given by following relation:

where ∆T is the change in temperature, V is the original volume, ∆V is the change in volume, and **α**** _{V}** is the

**coefficient of volume expansion**.

The** volumetric thermal expansion coefficient** for water is **not constant** over the temperature range and increases with the temperature (**especially at 300°C**), therefore the change in density is **not linear** with temperature (as indicated in the figure).

See also: Steam Tables

**At normal conditions** the total volume of coolant in the reactor coolant system is almost constant. On the other hand, **during transient load conditions** the **volume can significantly change**. These changes are naturally reflected in a change in pressurizer water level. When the average temperature of reactor coolant goes gradually down, the total water volume is also decreasing, which lowers the pressurizer level. On a gradual load pick-up, the increase in reactor coolant average temperature causes the total water volume to expand, which raises the pressurizer level. These effects must be controlled by pressurizer level control system.

## Control Volume – Control Volume Analysis

A **control volume** is a fixed region in space chosen for the thermodynamic study of mass and energy balances for flowing systems. The boundary of the **control volume** may be a real or imaginary **envelope**. The control surface is the boundary of the control volume.

A control volume analysis can be used for example to determine the rate of change of momentum for a fluid. In this analysis, we will consider a streamtube (**control volume**) as we did for the Bernoulli equation. In this** control volume** any change in momentum of the fluid within a control volume is due to the action of external forces on the fluid within the volume.

See also: Momentum Formula

As can be seen from the picture the **control volume method** can be used to analyze the law of conservation of momentum in fluid. **Control volume** is an **imaginary surface** enclosing a volume of interest. The control volume can be fixed or moving, and it can be rigid or deformable. In order to determine all forces acting on the surfaces of the control volume we have to solve the conservation laws in this control volume.

## Choosing a Control Volume

A control volume can be selected as any arbitrary volume through which fluid flows. This volume can be static, moving, and even deforming during flow. In order to solve any problem we have to solve basic conservation laws in this volume. It is very important to know all relative flow velocities to the control surface and therefore it is very important to define exactly the boundaries of the control volume during an analysis.

## Example: Water Jet Striking a Stationary Plate

**A stationary plate**(e.g. blade of a watermill) is used to deflect water flow at a velocity of**1 m/s**and at an angle of**90°**. It occurs at atmospheric pressure and the mass flow rate is equal to**Q =1 m ^{3}/s**.

**Calculate the pressure force.****Calculate the body force.****Calculate the total force.****Calculate the resultant force.**

**Solution**

- The
**pressure force**is zero as the pressure at both the inlet and the outlets to the control volume are atmospheric. - As the control volume is small we can ignore the
**body force**due to the weight of gravity. **F**= ρ.Q.(w_{x}_{1x}– w_{2x}) = 1000 . 1 . (1 – 0) =**1000 N****F**=_{y}**0****F**=**(1000, 0)**- The
**resultant force**on the plane is the same magnitude but in the opposite direction as the total force**F**(friction and weightareneglected).

The water jet exerts on the plate the force of **1000 N** in the x-direction.

References:

**Reactor Physics and Thermal Hydraulics:**

- J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading,MA (1983).
- J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
- W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
- Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering,Springer; 4th edition, 1994, ISBN:978-0412985317
- Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRCPress; 2edition, 2012, ISBN:978-0415802871
- Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN:978-3-319-13419-2
- Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition,John Wiley & Sons, 2006, ISBN:978-0-470-03037-0
- Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010,ISBN 978-1-4020-8670-0.
- U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER,AND FLUID FLOW.DOE Fundamentals Handbook,Volume 1, 2 and 3. June1992.

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### Related Posts

What is Specific Volume - Definition

What is Density - Physics - Definition

What is Pressure - Physics - Definition

## FAQs

### What is volume in physics short answer? ›

Definition. A volume is simply defined as **the amount of space occupied by any three-dimensional solid**. These solids can be a cube, a cuboid, a cone, a cylinder or a sphere.

**What does volume mean in physics? ›**

Volume is **the measure of the 3-dimensional space occupied by matter, or enclosed by a surface, measured in cubic units**. The SI unit of volume is the cubic meter (m^{3}), which is a derived unit.

**What is volume give answer? ›**

Volume is **the amount of space taken up by an object**, while capacity is the measure of an object's ability to hold a substance, like a solid, a liquid or a gas. ... Volume is measured in cubic units, while capacity can be measured in almost every other unit, including liters, gallons, pounds, etc.

**What is volume in science definition? ›**

Volume – **How much space an object or substance takes up**. • Measured in cubic meters (m3), liters (L) & milliliters (mL).

**What is volume example in physics? ›**

Volume is the measure of the capacity that an object holds. For example, **if a cup can hold 100 ml of water up to the brim, its volume is said to be 100 ml**. Volume can also be defined as the amount of space occupied by a 3-dimensional object.

**What is volume in physics for kids? ›**

Volume refers to **the amount of space the object takes up**. In other words, volume is a measure of the size of an object, just like height and width are ways to describe size. If the object is hollow (in other words, empty), volume is the amount of water it can hold. Try this at home: Take a large cup and a small cup.

**What is volume and mass in physics? ›**

**Mass is the physical quantity that signifies the amount of matter in the body of an object.** **Volume is the evaluation of how much 3-dimensional space is occupied by the object**. Mass is the physical value. Volume is the geometric value.

**What is volume of an object in physics? ›**

Volume of an object is **the quantity of three-dimensional space enclosed by a closed surface of that object**, for example, the space that a substance or shape occupies or contains.

**What is volume in one word? ›**

also : loudness. : the amount of space occupied by a three-dimensional object as measured in cubic units (such as quarts or liters) : **cubic capacity** see Metric System Table, Weights and Measures Table.

**What is volume in short form? ›**

(plural vols.) Abbreviation of volume.

### What is volume definition and formula? ›

Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The definition of length (cubed) is interrelated with volume.

**What is volume in physics class 11? ›**

As we know, volume is defined as **the physical quantity of a three- dimensional space enclosed by a closed surface**. If we take example: the space or shape occupied by the substance like solid, liquid, gas, or plasma. Also, volume is often numerically given by using the S.I derived unit, called the cubic meter.

**How do you find volume physics? ›**

Calculate the volume of the substance by dividing the mass of the substance by the density (**volume = mass/density**). Ensure the units are kept constant during the calculations.

**What is the definition of volume quizlet? ›**

volume. **the amount of space that an object takes up,or occupies**.

**What is volume 7th grade? ›**

Volume is **how much or the amount that can fit into a shape or space**. Remember area is how many squares can cover a space (square units), similarly, volume is how many cubes can fill a space (cubic units). Each 3D shape has a formula for finding volume.

**What is volume in mass? ›**

Volume equals **mass divided by density**; and. Mass equals density times volume.

**What is mass in physics? ›**

mass, in physics, **quantitative measure of inertia, a fundamental property of all matter**. It is, in effect, the resistance that a body of matter offers to a change in its speed or position upon the application of a force. The greater the mass of a body, the smaller the change produced by an applied force.

**What is volume vs mass with example? ›**

Mass and volume are two units used to measure objects. **Mass is the amount of matter an object contains, while volume is how much space it takes up**. Example: A bowling ball and a basketball are about the same volume as each other, but the bowling ball has much more mass.

**What is a sentence for volume? ›**

Use “volume” in a sentence

The radio is too loud. Turn the volume down. She picked up a thick volume and began to sing out loud.

**What is volume of liquid in physics? ›**

At its most basic level, volume is simply **a measure of space**. When measuring the volume of a liquid, sometimes referred to as capacity, the units liters (L) and milliliters (mL) are used. Devices used for this measurement include graduated cylinders, beakers, and Erlenmeyer flasks.

### What is volume of an object? ›

The volume of an object is **the amount of space occupied by the object or shape, which is in three-dimensional space**. It is usually measured in terms of cubic units. In other words, the volume of any object or container is the capacity of the container to hold the amount of fluid (gas or liquid).

**How do you find simple volume? ›**

Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is **length × width × height**. How you refer to the different dimensions does not change the calculation: you may, for example, use 'depth' instead of 'height'.

**What is volume in physics Brainly? ›**

**the amount of space that a substance or object occupies**.

**What two terms describe volume? ›**

The words **bulk and mass** are common synonyms of volume.

**What is mass and volume in physics? ›**

**Mass is the physical quantity that signifies the amount of matter in the body of an object.** **Volume is the evaluation of how much 3-dimensional space is occupied by the object**. Mass is the physical value. Volume is the geometric value.

**What is volume in Science 7th grade? ›**

Volume is **the measure of the amount of space that is occupied by matter**. A liquid is often measured in litres (L) or millilitres (mL).

**How to find the volume? ›**

The formula for volume is: **Volume = length x width x height**.

**How do you measure volume? ›**

The basic formula for understanding volume, such as the capacity of a rectangular container, is **length x width x depth**.

**What is volume vs density? ›**

Volume refers to the measurement of the amount of three-dimensional space occupied by an object. Unlike mass, volume changes according to the external conditions. Density refers to the mass contained in a substance for a given volume. It explains the relationship between mass and volume.

**How do you find volume in physics? ›**

Calculate the volume of the substance by dividing the mass of the substance by the density (**volume = mass/density**).