Answer:
k = 5406.88 N/m
Explanation:
Since the initial and final temperatures are constant while the gas expands, the expansion of the gas obeys Boyle's law
Initial gas pressure,
Let the initial gas volume = V
Volume = Length * Area
Since the cross sectional area does not change and the length of the gas-filled chamber is said to double, then the volume also doubles.
The final gas pressure, will be gotten from the Boyle's law equation
The Cross Sectional Area,
R = 5.33 cm = 0.0533 m
= 0.0089 m²
The force exerted on the piston, F = P₂ A
F = 1.145 * 10⁵ * 0.0089
F = 1021.9 N
To get the spring constant, use Hooke's law
F = k Δx
Where Δx = l₂ - l₁
Δx = 2l - l = l ( since the length of the chamber doubles on expansion)
Δx = 18.9 cm = 0.189 m
F = k Δx
1021.9 = k * 0.189
k = 1021.9/0.189
k = 5406.88 N/m