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

$𝑃 = 𝑃 _𝑎 + 𝑀 𝑔 / 𝐴$

where

P_{a} =

$P_a=$ atmospheric pressure

A =

$A=$ area of the cross-section of the piston.

M g =

$Mg=$ weight of the piston
Hence,

P =

$P=$ constant.
When temperature increases, as

P V = n R T

$PV = nRT$

\Rightarrow

$\Rightarrow$ the volume

(V)

$(V)$ increases at constant pressure.
Hence, option (3) is the correct answer.

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