A cylinder of cross-sectional area 12 cm2 is fitted with a piston, which is connected to a...

SKETCH:

The diagram shows a cylinder with a piston, which is connected to a spring.

RESEARCH

When the spring is compressed, the sum of the forces in the vertical direction can be equated to zero.

Let be the applied pressure. Then the force on the piston is

…… (1)

The initial volume of the gas is

Here is the height of the gas in the cylinder before the spring is compressed.

The final volume of the gas is

Here is the compression in the spring.

The Ideal gas law is given by

The Hooke’s law for the spring is

…… (2)

SIMPLIFY

Using Newton’s second law of motion, equating all the forces in the vertical direction to be zero, then the pressure of the gas is given by

…… (3)

Using Ideal gas law, the pressure of the gas is

…… (4)

Equating the equations (3) and (4), we have

…… (5)

From Ideal gas law, we have

Substituting the value of in equation (5), then

Let us consider,

Then the above quadratic equation can be written as

…… (6)

…… (7)

CALCULATE

The spring constant,

Number of moles,

Universal gas constant,

Initial temperature of the gas,

Area of the cylinder,

Atmospheric pressure,

Final temperature,

Substituting all the known values in the expression for, the value of is

Substituting all the known values in the expression for, the value of is

Substituting all the calculated values of, and in equation (6), the value of the compression is

The negative sign of the answer in -0.2444 m is not a right answer as it indicates that the spring is stretched. But in the given situation the spring is compressed hence the correct answer is