Given are statements for certain thermodynamic variables,
(A) Internal energy, volume (V) and mass (M) are extensive variables.
(B) Pressure (P), temperature ( T ) and density ( ρ ) are intensive variables.
(C) Volume (V), temperature (T) and density ( ρ ) are intensive variables.
(D) Mass (M), temperature (T) and internal energy are extensive variables.
Choose the correct answer from the options given below :

Solution

Physics sir · 3 steps

Cut the system in half in your head: whatever halves is extensive, whatever stays the same is intensive.

1. The halving test. Divide a uniform system into two equal halves. A quantity that also halves is extensive. A quantity that stays the same in each half is intensive.

   Variable	In each half	Type
   Mass M	halves	extensive
   Volume V	halves	extensive
   Internal energy U	halves	extensive
   Pressure P	same	intensive
   Temperature T	same	intensive
   Density ρ = M/V	same	intensive

2. Check each statement. (A) is correct: U, V and M all halve. (B) is correct: P, T and ρ do not change. (C) is wrong because V is extensive. (D) is wrong because T is intensive.
3. So. Only (A) and (B) are correct, which is option (b).

The idea to keep. Extensive quantities add up when you join systems, intensive ones do not. The ratio of two extensive quantities, like density = M/V, is always intensive.

Answer from the NTA final answer key. Solution by PrepWiser.