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Question
The pressure of a gas kept in an isothermal container is 200 kPa. If half the gas is removed from it, the pressure will be
Options
100 kPa
200 kPa
400 kPa
800 kPa
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Solution
100 kPa
Let the number of moles in the gas be n.
Applying equation of state, we get
\[PV = nRT\]
\[ \Rightarrow P = \frac{nRT}{V}\]
\[ \Rightarrow 2 \times {10}^5 = \frac{nRT}{V} . . . \left( 1 \right)\]
\[\text { When half of the gas is removed, number of moles left behind } = \frac{n}{2}\] \[\text { Let the pressure be P' }. \]
\[P' = \frac{n}{2}\frac{RT}{V}\]
\[\text { Now }, \]
\[P' = \frac{1}{2} \times 2 \times {10}^5 = {10}^5 \left[ \text { From eq } . \left( 1 \right) \right]\]
=100 kPa
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