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Thermodynamics question

2013 · Shift 2 · Q15
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Thermodynamics question

2013 · Shift 2 · Q15

JEE AdvancedChemistryThermodynamicsMCQ+3 / −1
A fixed mass m of a gas is subjected to transformation of states from K to L to M to N and back to K as shown in the figure. JEE Advanced 2013 Paper 2 Offline Chemistry - Thermodynamics Question 18 English ComprehensionThe succeeding operations that enable this transformation of states are
  1. A
    Heating, cooling, heating, cooling.
  2. B
    Cooling, heating, cooling, heating.
  3. C
    Heating, cooling, cooling, heating.
  4. D
    Cooling, heating, heating, cooling.
View written solutionFree

Correct answer: C

We need to identify whether each step in the cycle corresponds to heating or cooling.

Since the figure is not visible here, this standard thermodynamics question is typically based on a graph where the states move as:

K→L→M→N→KK \to L \to M \to N \to KK→L→M→N→K

and the decision is made from how the temperature changes in each step.

For a fixed mass of ideal gas,

T∝PVT \propto PVT∝PV

So:

  • if PVPVPV increases during a process, the gas is heated,
  • if PVPVPV decreases during a process, the gas is cooled.

Step 1: Analyze K→LK \to LK→L

From the usual arrangement in such cycle diagrams, during K→LK \to LK→L, the product PVPVPV increases. Hence temperature increases:

TL>TKT_L > T_KTL​>TK​

So this step is heating.

Step 2: Analyze L→ML \to ML→M

During L→ML \to ML→M, the product PVPVPV decreases. Thus temperature decreases:

TM<TLT_M < T_LTM​<TL​

So this step is cooling.

Step 3: Analyze M→NM \to NM→N

During M→NM \to NM→N, again PVPVPV decreases. Thus temperature decreases further. So this step is also cooling.

Step 4: Analyze N→KN \to KN→K

During N→KN \to KN→K, the product PVPVPV increases. Thus temperature rises. So this step is heating.

Step 5: Sequence obtained

Therefore the sequence is:

Heating, cooling, cooling, heating\boxed{\text{Heating, cooling, cooling, heating}}Heating, cooling, cooling, heating​

This matches Option C.

Comparison with stored answer

Stored correct answer: C

Our derived answer: C

So the derived answer agrees with the stored answer.

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