## Expansivity

This is defined as amount a material expands or contracts per unit length, per-degree change in temperature.The addition of heat will usually cause expansion of the body. during expansion, the dimension of the body increases.

### Areas covered

- concept of thermal expansivity
- Linear Expansion
- Linear Expansivity
- Area expansivity
- Cubic or volume expansivity
- Questions and solutions

### 1) Concept of thermal expansivity

When heated most solid and liquid expand. they also contract when cooled. Expansion means an increase in size of object. According to kinetic molecular theory, when an object is heated the molecule acquire more kinetic energy which enable them to overcome intermolecular forces. Therefore, the vibration of the molecule increases and their displacement mean position increases. As a result of this, the average distance between the molecules of the substance leading to an increase in size of the substance.

#### 2) Linear Expansion

Different solid expands by different amount when heated over the same temperature range. Copper for example expands more than steel, when both are heated through the same rise in temperature. This is because they have different coefficient of linear expansion.

#### 3) Linear Expansivity (α)

The linear expansivity of a substance is defined as an
increase in length, per-unit length, per degree rise in temperature. In
symbols.

This is equivalent to;

Where, α = linear expansivity, L

_{1 }= initial length, L_{2}= final length, ɵ_{2}= final temperature, ɵ_{1}= initial temperature.
L

_{2}– L_{1 }= expansion
L

_{2 }= L_{1}(αɵ_{1}+ 1)
The unit of linear
expansivity is per-degree or per-kelvin.

### 4) Area expansivity

Area expansivity is the increase in area, per unit area, per degree rise in temperature for a plate of initial area (A

_{I}), which expands to the final area (A_{f}) upon a temperature rise ∆ɵ
β = 2α

therefore, A

_{f }= A_{I}(2αɵ + 1)### 5) Cubic expansivity (ɤ)

Cubic or volume expansivity of a solid, liquid or gas is the increase in volume, per-unit volume, per-degree rise in temperature.ɤ = 3 α

I.e 3 α =

3 α V

_{I}ɵ = V_{F}– V_{I}
V

_{F}= V_{I}(3αɵ + 1)#### Questions and solutions

1) A copper rod whose length at 30°c is 10m is heated
to 50°c. Find the new length. (Take α as 0.000017 K

^{-1})Solution

Recall for linear expansivity, L

_{2 }= L_{1}(αɵ_{1}+ 1)
ɵ = 50°c - 30°c = 20°c

L

_{2}= 10(0.000017(20) + 1) = 10.0034m2) Explain the statement that the linear expansivity of brass is 0.000019 k

^{-1}. A brass rod 90cm long at 28°c is heated to 98°c. Find the change in length of a rod.

solution

L

_{2 }= L_{1}(αɵ_{1}+ 1)
ɵ = 98°c - 28°c = 70°c

L

_{2}= 90(0.000019(70) + 1) = 90.1197cm3) Describe an experiment to measure the linear expansivity of copper in the form of rod. Calculate the expansion of 10m of copper rod when heated from 10°c to 80°c . Take the linear expansivity of copper as 0.000017.

Solution

L

_{2 }= L_{1}(αɵ_{1}+ 1)
ɵ = 80°c - 10°c = 70°c

L

_{2}= 10(0.000017(70) + 1) = 10.0119
4) An iron rod is 1.58m long at 0°c. What must be
the length of a brass rod at 0°c if the the difference between the lengths of
the two rods is to remain the same at all temperatures.

Solution

Brass rod = L

_{1 }
Iron rod = 1.58m

α (brass rod) = 0.000019 K

^{-1}
α (iron rod) = 0.000012 K

^{-1}
Linear expansivity difference =
0.000007 k

^{-1}
thanks now i understand

ReplyDeleteCould there be videos fun, cartoonish that will make your website more intresting

ReplyDeleteQuestion 4 is not clear. please explain further

ReplyDeleteThe change in length and temperature between brass and Iron is the same. That is α[iron]L(iron)= α(brass)L(brass)

DeleteL(brass)= α(iron)xL(iron)/α(brass)

A Metal Of Length 15.01 M Is Heated Until Its Temperature Rises By 60degree Celisus. If Its New Length Is 15.05cm, Calculate Its Linear Expansivity,

ReplyDelete*please Explain It*

Is L2 = 15.05m or cm

DeletePlease reply so I can proceed with the explanation.

DeleteIt 3. 061k-1

DeleteIn linear expansivity, the final length is always greater than the initial length. This fact makes the question itself wrong because L1=15.01m while L2=15.05cm = 0.1505m, ie L1>L2, which is not possible in linear expansivity.

Delete