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Heat and Thermodynamics question

2023 · 24 Jan · Shift 2 · Q53
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  5. /2023 · 24 Jan · Shift 2 · Q53

Heat and Thermodynamics question

2023 · 24 Jan · Shift 2 · Q53

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1
In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; T3>T2>T1\mathrm{T_3 \gt T_2 \gt T_1}T3​>T2​>T1​ as :
  1. A
    JEE Main 2023 (Online) 24th January Evening Shift Physics - Heat and Thermodynamics Question 125 English Option 1
  2. B
    JEE Main 2023 (Online) 24th January Evening Shift Physics - Heat and Thermodynamics Question 125 English Option 2
  3. C
    JEE Main 2023 (Online) 24th January Evening Shift Physics - Heat and Thermodynamics Question 125 English Option 3
  4. D
    JEE Main 2023 (Online) 24th January Evening Shift Physics - Heat and Thermodynamics Question 125 English Option 4
View written solutionFree

Correct answer: B

  1. In an isothermal process, the temperature remains constant.

  2. For an ideal gas, the equation is PV=nRTPV = nRTPV=nRT

  3. Since TTT is constant for a given isotherm, we get PV=constantPV = \text{constant}PV=constant Hence, P=constantVP = \frac{\text{constant}}{V}P=Vconstant​

  4. Therefore, the PPP-VVV graph for an isothermal change is a rectangular hyperbola.

  5. Now compare the three temperatures: T3>T2>T1T_3 > T_2 > T_1T3​>T2​>T1​

    For the same amount of gas, PV=nRTPV = nRTPV=nRT At a given volume VVV, P∝TP \propto TP∝T So for the same volume, P3>P2>P1P_3 > P_2 > P_1P3​>P2​>P1​

  6. This means the isotherm corresponding to higher temperature lies above the lower temperature isotherm on the PPP-VVV diagram.

  7. So the correct figure must show:

    • three hyperbolas,
    • with T3T_3T3​ highest,
    • then T2T_2T2​,
    • then T1T_1T1​ lowest.
  8. Among the given options, this corresponds to Option B.

Therefore, the correct answer is: B\boxed{\text{B}}B​

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