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Thermodynamics question

2017 · 9 Apr · Shift 1 · Q19
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Thermodynamics question

2017 · 9 Apr · Shift 1 · Q19

JEE MainChemistryThermodynamicsMCQ+4 / −1
A gas undergoes change from state A to state B. In this process, the heat absorbed and work done by the gas is 5 J and 8 J, respectively. Now gas is brought back to A by another process during which 3 J of heat is evolved. In this reverse process of B to A :
  1. A
    10 J of the work will be done by the gas.
  2. B
    6 J of the work will be done by the gas.
  3. C
    10 J of the work will be done by the surrounding on gas.
  4. D
    6 J of the work will be done by the surrounding on gas.
View written solutionFree

Correct answer: D

  1. Use the first law of thermodynamics

    Taking the chemistry sign convention: ΔU=q−w\Delta U = q - wΔU=q−w where:

    • qqq = heat absorbed by the gas
    • www = work done by the gas

  2. From state A to state B

    Given:

    • Heat absorbed, qAB=+5 Jq_{AB} = +5\,\text{J}qAB​=+5J
    • Work done by gas, wAB=+8 Jw_{AB} = +8\,\text{J}wAB​=+8J

    Therefore, ΔUAB=qAB−wAB=5−8=−3 J\Delta U_{AB} = q_{AB} - w_{AB} = 5 - 8 = -3\,\text{J}ΔUAB​=qAB​−wAB​=5−8=−3J

    So, UB−UA=−3 JU_B - U_A = -3\,\text{J}UB​−UA​=−3J

  3. For the reverse process B to A

    Since internal energy is a state function, ΔUBA=−ΔUAB=+3 J\Delta U_{BA} = -\Delta U_{AB} = +3\,\text{J}ΔUBA​=−ΔUAB​=+3J

    Also, during B→AB \to AB→A, 3 J of heat is evolved, so heat leaves the gas: qBA=−3 Jq_{BA} = -3\,\text{J}qBA​=−3J

  4. Apply first law to B to A

    ΔUBA=qBA−wBA\Delta U_{BA} = q_{BA} - w_{BA}ΔUBA​=qBA​−wBA​

    Substituting values: 3=−3−wBA3 = -3 - w_{BA}3=−3−wBA​

    −wBA=6-w_{BA} = 6−wBA​=6

    wBA=−6 Jw_{BA} = -6\,\text{J}wBA​=−6J

  5. Interpret the sign of work

    Negative www means work is done on the gas by the surroundings.

    Magnitude of work = 6 J6\,\text{J}6J.

  6. Check options

    • A: 10 J done by gas →\rightarrow→ incorrect
    • B: 6 J done by gas →\rightarrow→ incorrect
    • C: 10 J done by surroundings on gas →\rightarrow→ incorrect
    • D: 6 J done by surroundings on gas →\rightarrow→ correct

Hence, the correct option is D.

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