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Heat and Thermodynamics question

2021 · 18 Mar · Shift 2 · Q59
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  5. /2021 · 18 Mar · Shift 2 · Q59

Heat and Thermodynamics question

2021 · 18 Mar · Shift 2 · Q59

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1
An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is S1 and that of the other part is S2. Given that S1 > S2. If the piston is removed then the total entropy of the system will be :
  1. A
    S1 −-− S2
  2. B
    S1S2{{{S_1}} \over {{S_2}}}S2​S1​​
  3. C
    S1 ×\times× S2
  4. D
    S1 + S2
View written solutionFree

Correct answer: D

  1. Identify the situation

    The gas is divided into two parts by a piston. The entropy of the two parts is given as: S1andS2S_1 \quad \text{and} \quad S_2S1​andS2​ with S1>S2S_1 > S_2S1​>S2​

  2. Use the property of entropy

    Entropy is an extensive property. This means that for two parts of a system, the total entropy is the sum of the entropies of the parts: Stotal=S1+S2S_{\text{total}} = S_1 + S_2Stotal​=S1​+S2​

  3. Effect of removing the piston

    When the piston is removed, the two parts become a single system. Since entropy adds for subsystems, the total entropy of the combined system is: S=S1+S2S = S_1 + S_2S=S1​+S2​

  4. Check options

    • A: S1−S2S_1 - S_2S1​−S2​ — incorrect, entropy does not subtract.
    • B: S1S2\dfrac{S_1}{S_2}S2​S1​​ — incorrect, entropy is not combined as a ratio.
    • C: S1×S2S_1 \times S_2S1​×S2​ — incorrect, entropy is not multiplicative.
    • D: S1+S2S_1 + S_2S1​+S2​ — correct.

  5. Final answer

    S1+S2\boxed{S_1 + S_2}S1​+S2​​

So, the correct option is D.

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