Question

1. A gas fills the right portion of a horizontal cylinder whose radius is 4.60 cm. The initial pressure of the gas is 1.01 X 10Pa. A frictionless movable piston separates the gas from the left portion of the cylinder, which is evacuated and contains an ideal spring, as the figure shows. The piston is initially held in place by a pin. The spring is initially unstrained, and the length of the gas-filled portion is 23.0 cm. When the pin is removed and the gas is allowed to expand, the length of the gas-filled chamber doubles. The initial and final temperatures are equal. Determine the spring constant of the spring. * 1867 N/m Unstrained Spring Pin

Answer 1

Given is:-

Initial Pressure  

P1 = 1.01 x 10 Pa

Radius of the cylinder  
T= 4.60cm
or
r=0.0460m

Initial length of the gas filled portion of the cylinder is

Li = 0.23m

Now,

After expansion the length of the gas filled portion is

L2 = 2 x 0.23m = 0.46m

Let the initial volume V₁ and the final volume V₂

We know that from the ideal gas equation

PV EV, Ti Т)

but the temperature are equal therefore

PIVA = P2V2

or

P1(ALI) = P2(AL2)

or

PILI) = P2(L2)

by plugging all the values we get

1.01 x 10 Pa(0.23m) = P2(0.46m)

which gives us

P = 50500Pa

Thus

the force on the piston and spring is

F= PA

thus

F = (50500 Pa) ((0.0460m2)

which gives us

F = 335.704N

The stretched distance is

AT= 0,23m

thus

F=k

or

335.704N = K (0.23m)

which gives us the value of spring constant, which is

K = 1459.58N/m