Statement I: A sample of gas is heated at constant pressure from $200 K$ to $400 K$ and its volume doubles.
Statement II: Each molecule expands to twice its original volume.

Both Statement I and Statement II are correct and Statement II is the correct explanation of Statement I.

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Both Statement I and Statement II are correct, but Statement II is not the correct explanation of Statement I.

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Statement I is correct, but Statement II is incorrect.

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Statement I is incorrect, but Statement II is correct.

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Solution

The correct option is C Statement I is correct, but Statement II is incorrect.
Option C is the correct answer.
Statement 1 is true. Ideal gas equation can be written as $P V$ = $n R T$
When the temperature of the gas is $200 K$ , the equation can be written as $P V$ = $200 n R$
Thus, $V$ = $\frac{200 n R}{P}$
Now, when the temperature of the gas is increased to $400 K$ , the equation can be written as $P V$ = $400 n R$
Thus, $V$ = $\frac{400 n R}{P}$
which can further be written as $V$ = $2$ $*$ $\frac{200 n R}{P}$
That is, twice the volume as in the case of 200 K.
This is possible when pressure of the gas is kept constant.
Statement 2 is false. Total volume of the gas increases but size of the molecule remains the same. Volume of molecule doesn't change. Only the total volume of the gas increases.

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Statement I: A sample of gas is heated at constant pressure from 200K to 400K and its volume doubles.Statement II: Each molecule expands to twice its original volume.

Statement I: A sample of gas is heated at constant pressure from $200 K$ to $400 K$ and its volume doubles.
Statement II: Each molecule expands to twice its original volume.