Verified Solution • 2025–26 Session moderate

QJEEM19Chad99: JEE Main 2019 Chemistry - Class 11 JEEM19Chad99 Solution: Two blocks of the same metal having same mass and at…

Two blocks of the same metal having same mass and at temperature T1 and T2, respectively, are brought in contact with each other and allowed to attain thermal equilibrium at constant pressure. The change in entropy, Δ\Delta S, for this process is :

Multiple Choice Options

  • A 2Cp In [(T1+T2)12T1T2]\left[ {{{{{\left( {{T_1} + {T_2}} \right)}^{{1 \over 2}}}} \over {{T_1}{T_2}}}} \right]
  • B 2Cp In [(T1+T2)2T1T2]\left[ {{{\left( {{T_1} + {T_2}} \right)} \over {2{T_1}{T_2}}}} \right]
  • C Cp In [(T1+T2)24T1T2]\left[ {{{{{\left( {{T_1} + {T_2}} \right)}^2}} \over {4{T_1}{T_2}}}} \right]
  • D 2Cp In [(T1+T2)4T1T2]\left[ {{{\left( {{T_1} + {T_2}} \right)} \over {4{T_1}{T_2}}}} \right]

Step-by-Step Verified Solution

When two blocks comes in contact with each other and attain thermal equilibrium then

final temperature of the blocks,

Tf = T1+T22{{{T_1} + {T_2}} \over 2}

Δ\Delta S = Δ\Delta S1 + Δ\Delta S2

= Cp ln⁡(TfT1)\ln \left( {{{{T_f}} \over {{T_1}}}} \right) + Cp ln⁡(TfT2)\ln \left( {{{{T_f}} \over {{T_2}}}} \right)

= Cp ln⁡(T1+T22T1)\ln \left( {{{{T_1} + {T_2}} \over {2{T_1}}}} \right) + Cp ln⁡(T1+T22T2)\ln \left( {{{{T_1} + {T_2}} \over {2{T_2}}}} \right)

= Cp ln⁡((T1+T2)24T1T2)\ln \left( {{{{{\left( {{T_1} + {T_2}} \right)}^2}} \over {4{T_1}{T_2}}}} \right)

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