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Thermodynamics question

2023 · 30 Jan · Shift 1 · Q17
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  5. /2023 · 30 Jan · Shift 1 · Q17

Thermodynamics question

2023 · 30 Jan · Shift 1 · Q17

JEE MainChemistryThermodynamicsNumerical+4 / −1
When 2 litre of ideal gas expands isothermally into vacuum to a total volume of 6 litre, the change in internal energy is ‾\underline{\hspace{2cm}}​ J. (Nearest integer)
Numerical answer
View written solutionFree

Correct answer: 0

  1. Given

    • Initial volume: V1=2 LV_1 = 2\,\text{L}V1​=2L
    • Final volume: V2=6 LV_2 = 6\,\text{L}V2​=6L
    • Process: isothermal expansion into vacuum (free expansion)
    • Gas: ideal gas

  2. Key thermodynamic fact for an ideal gas The internal energy of an ideal gas depends only on temperature.

    U=U(T)U = U(T)U=U(T)

    Therefore,

    ΔU=nCVΔT\Delta U = nC_V\Delta TΔU=nCV​ΔT

  3. Since the process is isothermal Isothermal means temperature remains constant, so

    ΔT=0\Delta T = 0ΔT=0

    Hence,

    ΔU=nCV(0)=0\Delta U = nC_V(0) = 0ΔU=nCV​(0)=0

  4. Conclusion The change in internal energy is

    0 J\boxed{0\,\text{J}}0J​

  5. Comparison with stored answer Stored correct answer = 000

    Our derived answer = 000

    So they agree.

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