## Thursday, January 5, 2017

### Expansion of Liquids Problems with Solutions

We are solving series of problems basing on the concept expansion of liquids. The molecular force of attraction among liquid is comparatively less than that of solids. When heat energy is given to a solid, the recovery of molecules back to their original position is less probable than solids and hence expansion of liquids is more than that of solids. There is no specific length and area of cross section for a liquid and hence there is no linear and areal expansion. Expansion of liquids is studies only in terms of volume expansion. Liquid has to be taken in a container and the container will first absorb heat energy and it expands first. So the expansion of liquid appears to be different from real expansion and hence we need to study liquid expansion in terms of apparent and real expansions and to measure them we have different expansion coefficients.

Problem

A liquid is heated in a vessel and the relation between apparent and real expansion coefficients is given to us as shown in the diagram below. We need to find the coefficient of linear expansion of the solid container.

Solution

We know that the liquid has two different types of coefficients called real expansion coefficient and apparent expansion coefficient. When the container expands with the rise in temperature, real expansion coefficient is more than that of apparent expansion coefficient. We also know that the coefficient of real expansion is the sum of coefficient of apparent expansion and the volume expansion coefficient of solid container. Substituting the given data of the problem, it can be solved as shown in the diagram below.

Problem

Coefficient of real expansion of the liquid are given to us in the problem and coefficient of linear expansion of the material is also given to us in the data. We need to find the coefficient of apparent expansion of the liquid and the problem is as shown in the diagram below.

Solution

We know the relation between the apparent and real expansion coefficients and we can use it to solve the problem as done in the previous problem. Solution is as shown in the diagram below.

Problem

Coefficients of apparent expansion of a liquid in two different vessels is given to us and we need to find the difference between the coefficients of linear expansion coefficients and the problem is as shown in the diagram below.

Solution

As the liquid is same in both the cases, its coefficient of real expansion is same and it can be equated in both the cases basing on the definition.Solution is as shown in the diagram below.

Problem

There is certain mass of the liquid at a given temperature and there is some overflow of liquid when there is raise in the temperature. We need to find the coefficient of apparent expansion of the liquid and the problem is as shown in the diagram below.

Solution

We can express coefficient of apparent expansion of the liquid as the ratio of mass of the liquid over flown due to raise of the temperature to the remaining mass of the liquid after over flown. Taking that into consideration, we can solve the problem as shown in the diagram below.

Problem

A specific gravity bottle has certain mass of liquid in it at certain temperature and when the temperature is raised to a certain value, we need to know the mass of the liquid expelled and the problem is as shown in the diagram below.

Solution

We can solve the problem based on the definition of coefficient of apparent expansion of the liquid. We know that it can be the ratio of mass of the liquid expelled to the mass remaining after the raise of the temperature. Solution is as shown in the diagram below.

Problem

There is some mercury in a glass vessel of one liter volume and its volume remains constant in the vessel at all temperature and we need to find the volume of the mercury filled so that its volume appears constant at all temperatures. Problem is as shown in the diagram below.

Solution

For the level to remain constant at all temperatures, the expansion of mercury shall be similar to expansion of glass vessel. Taking that definition into consideration, we can solve the problem as shown in the diagram below.

Problem

A body is floating in the water with 98 % immersed at 4 degree centigrade. We need to know at what temperature the body completely gets immersed in the liquid and the problem is as shown in the diagram below.

Solution

We can use the definition of coefficient of apparent expansion as shown in the diagram below and solve the problem.

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