Ncert Exercises & Solutions

A cylinder containing an ideal gas is in a vertical position and has a piston of mass \(M\) that is able to move up or down without friction (figure). If the temperature is increased,

1.	both \(P\) and \(V\) of the gas will change.
2.	only \(P\) will increase according to Charles' law.
3.	\(V\) will change but not \(P.\)
4.	\(P\) will change but not \(V.\)

Hint: The pressure remains the same.

Step: Find the change in volume.

Consider the diagram where an ideal gas is contained in a cylinder, having a piston of mass M. Friction is absent.

The pressure inside the gas will be,

\( 𝑃 = 𝑃 _𝑎 + 𝑀 𝑔 / 𝐴\)

where \(P_a=\) atmospheric pressure
\(A=\) area of the cross-section of the piston.
\(Mg=\) weight of the piston
Hence, \(P=\) constant.
When temperature increases, as \(PV = nRT \)
\(\Rightarrow \) the volume \((V)\) increases at constant pressure.
Hence, option (3) is the correct answer.

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