Given below are two statements: one is labelled as Assertion (A)...

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : An ideal gas is enclosed within a container fitted with a piston. When volume of this enclosed gas is increased at constant temperature. The pressure exterted by gas on piston decreases. Reason (R) : In the above situation, the rate of molecuels per unit area striking on the piston decreases. In the light of the above statements, choose the most appropriate answer from the options given below:

Options

ABoth (A) and (R) are true and (R) is the correct explanation of (A).
BBoth (A) and (R) are true and (R) is NOT the correct explanation of (A).
C(A) is true but (R) is false.
D(A) is false but (R) is true.

Correct answer

A. Both (A) and (R) are true and (R) is the correct explanation of (A).

Step-by-step solution

(\frac{\mathrm{p} }{\rho}=\frac{\mathrm{RT}}{\mathrm{Mw}}

\Rightarrow

\mathrm{p}=

\left(\frac{\mathrm{M}}{\mathrm{V}

}\right)\left(\frac{\mathrm{RT}}{\mathrm{Mw}}\right)

at constant temperature (\Rightarrow \mathrm{p} \propto \frac{1}{\mathrm{ V}}) (\mathrm{V} \uparrow) and (\mathrm{P} \downarrow)

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