One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the P-V diagram. Column II gives the characteristics involved in the cycle. Match them with each of the processes given in Column I.
Column I (A) Process A → B (B) Process B → C (C) Process C → D (D) Process D → A
Column II (p) Internal energy decreases. (q) Internal energy increases. (r) Heat is lost. (s) Heat is gained. (t) Work is done on the gas.
Answer: A → I, A → III, A → V, B → I, B → III, C → II, C → IV, D → III, D → V
Solution
Process A→B: Isobaric compression — volume decreases, so temperature decreases (U decreases), work done on gas, heat lost. Process B→C: Isochoric — volume constant, pressure decreases, so temperature decreases (U decreases), no work, heat lost. Process C→D: Isobaric expansion — volume increases, temperature increases (U increases), work done by gas, heat gained. Process D→A: Polytropic with T_A = T_D — internal energy unchanged overall, but analyzing the path shows heat lost and work done on gas.
JEE Advanced · 2011 · 10 Apr 2011 · Paper 2 · Match the columns
