Example 2: Equation of state for ideal gas
Example : In a gas-spring system
|An ideal gas is contained in a cylinder. Initially the pressure, volume and temperature were P1, V1, and T1.
A spring with a spring constant k attaches to the piston as the figure.
The area of piston is A.
The gas expands against the spring by increasing temperature to at constant pressure T2.
What is the displacement?
Let final displacement as Δx
We can address this problem by two approaches; the force balances or the energy balances.
① Force balance at the piston
The force exerted by the spring due to the displacement is balanced with the gas pressure
Ideal gas law holds for all ideal gas
② Energy balance
Work done by the gas = Energy stored in spring