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A thermally insulating horizontal tube of cross-sectional area A is filled with a

volume 2V of gas at a pressure p. At the centre of the tube is a freely sliding piston

of mass M which seals the left and right hand sides of the tube from each other (i.e.

at equilibrium there is a volume V either side of the piston).

The piston is given a small displacement x to the left and then released. Assuming

that friction has a negligible effect over many cycles:

(i) Show that the force F on the piston is given by:

F=[tex]\frac{-2xpA^2}{\gamma V}[/tex]

[tex]\gamma[/tex]= C_p/ C_v

ii) and comment on the nature of the motion. {1}

(iii) Derive the expression for [tex]\omega[/tex] the frequency of oscillation.

volume 2V of gas at a pressure p. At the centre of the tube is a freely sliding piston

of mass M which seals the left and right hand sides of the tube from each other (i.e.

at equilibrium there is a volume V either side of the piston).

The piston is given a small displacement x to the left and then released. Assuming

that friction has a negligible effect over many cycles:

(i) Show that the force F on the piston is given by:

F=[tex]\frac{-2xpA^2}{\gamma V}[/tex]

[tex]\gamma[/tex]= C_p/ C_v

ii) and comment on the nature of the motion. {1}

(iii) Derive the expression for [tex]\omega[/tex] the frequency of oscillation.

**3. I don't know how to start this, as the gas is not Ideal I have no idea what formulas to apply to it. I know that Q=0 and think the work done =0. Is this right? Can somebody please help me get started?**
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