Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the 4×4 matrix given in the ORS.
Column I
Column II
(A) An insulated container has two chambers separated by a valve. Chamber I contains an ideal gas and the Chamber II has vacuum. The valve is opened. (see structure)
(p) The temperature of the gas decreases
(B) An ideal monoatomic gas expands to twice its original volume such that its pressure P∝V21, where V is the volume of the gas
(q) The temperature of the gas increases or remains constant
(C) An ideal monoatomic gas expands to twice its original volume such that its pressure P∝V4/31, where V is its volume
(r) The gas loses heat
(D) An ideal monoatomic gas expands such that its pressure P and volume V follows the behaviour shown in the graph (see structure)
(s) The gas gains heat
AD
Answer: A → II, B → I, B → III, C → I, C → IV, D → II, D → IV
Solution
Matching based on thermodynamic processes:
(A) → (q): Free expansion into vacuum is adiabatic with no work done, so temperature remains constant.
(B) → (p) & (r): For P∝1/V2, using PV=nRT, we get T∝1/V. As volume doubles, temperature halves (decreases). Since ΔU<0 and W>0, by first law Q=ΔU+W<0 (loses heat).
(C) → (p) & (s): For P∝1/V4/3, this is an adiabatic process (PVγ=const with γ=4/3). Temperature decreases during adiabatic expansion, but the question asks about heat exchange. For adiabatic process, Q=0, but the source solution indicates (s), which needs verification.
(D) → (q) & (s): The graph shows an expansion process. If temperature increases or remains constant during expansion, the gas must gain heat.
JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Match the columns
