$X$ is an extensive property and $x$ is an intensive property of a thermodynamic system. Which of the following statement$(s)$ is (are) correct?

  • A
    $xX$ is extensive
  • B
    $\frac{x}{X}$ is intensive
  • C
    $\frac{X}{x}$ is extensive
  • D
    $\frac{dX}{dx}$ is intensive

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An ideal gas is allowed to expand against a constant pressure of $2 \ bar$ from $10 \ L$ to $50 \ L$ in one step. Calculate the amount of work done by the gas. If the same expansion were carried out reversibly,will the work done be higher or lower than the earlier case? (Given that $1 \ L \ bar = 100 \ J$)

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$(ii)$ $1 \text{ calorie} = ........ \text{ Joules}$.
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