Skip main navigation

New offer! Get 30% off one whole year of Unlimited learning. Subscribe for just £249.99 £174.99. New subscribers only. T&Cs apply

Find out more

Example 2: Equation of state for ideal gas

Equation of state for adiabatic, reversible expansion of 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

        (F)=(kΔx)=(P)gas(A)=(P)1(A)
    Ideal gas law holds for all ideal gas

② Energy balance
    Work done by the gas = Energy stored in spring

This article is from the free online

Thermodynamics in Energy Engineering

Created by
FutureLearn - Learning For Life

Reach your personal and professional goals

Unlock access to hundreds of expert online courses and degrees from top universities and educators to gain accredited qualifications and professional CV-building certificates.

Join over 18 million learners to launch, switch or build upon your career, all at your own pace, across a wide range of topic areas.

Start Learning now