Given are statements for certain thermodynamic variables,

(A) Internal energy, volume $(\mathrm{V})$ and mass $(\mathrm{M})$ are extensive variables.

(B) Pressure (P), temperature ( T ) and density ( $\rho$ ) are intensive variables.

(C) Volume (V), temperature (T) and density ( $\rho$ ) are intensive variables.

(D) Mass (M), temperature (T) and internal energy are extensive variables.

Choose the correct answer from the options given below :

<p><p><strong>Check Statement (A)</strong>: </p> <p>“Internal energy (U), volume (V), and mass (M) are extensive variables.” </p></p> <p><p><strong>Internal energy</strong> is extensive. </p></p> <p><p><strong>Volume</strong> is extensive. </p></p> <p><p><strong>Mass</strong> is extensive. </p> <p>Hence, statement (A) is <strong>correct</strong>.</p></p> <p><p><strong>Check Statement (B)</strong>: </p> <p>“Pressure (P), temperature (T), and density (ρ) are intensive variables.” </p></p> <p><p><strong>Pressure</strong> is intensive. </p></p> <p><p><strong>Temperature</strong> is intensive. </p></p> <p><p><strong>Density</strong> is intensive. </p> <p>Hence, statement (B) is <strong>correct</strong>.</p></p> <p><p><strong>Check Statement (C)</strong>: </p> <p>“Volume (V), temperature (T), and density (ρ) are intensive variables.” </p></p> <p><p><strong>Volume</strong> is <strong>not</strong> intensive; it is an extensive property. </p></p> <p><p>(T) and (ρ) are indeed intensive. </p> <p>Since volume is miscategorized here, (C) is <strong>incorrect</strong>.</p></p> <p><p><strong>Check Statement (D)</strong>: </p> <p>“Mass (M), temperature (T), and internal energy are extensive variables.” </p></p> <p><p><strong>Mass</strong> is extensive. </p></p> <p><p><strong>Temperature</strong> is <strong>not</strong> extensive (it is intensive). </p></p> <p><p><strong>Internal energy</strong> is extensive. </p> <p>Because temperature is miscategorized, (D) is <strong>incorrect</strong>.</p></p> <p>Only <strong>(A)</strong> and <strong>(B)</strong> are correct statements. </p> <p>Therefore, the correct choice is:</p> <blockquote> <p><strong>Option B: (A) and (B) Only.</strong></p> </blockquote>