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 \(V.\)

3. Hint: The pressure remains the same.

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

Step 1: Find the change in volume.

The pressure inside the gas will be,

P = P_{a} + M g / A

where

P_{a}

= atmospheric pressure
A = area of cross-section of the piston.
Mg = weight of the piston
Hence, P = constant.
When temperature increases, as PV = nRT

\Rightarrow

volume (V) increases at constant pressure.

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