Two bolcks to the same metal having same mass and at temperature `T_1` and `T_2` respectively ,are brought in contact with each other and allowed to attain thermal equilibrium at constant pressure .The change in entropy ,`Delta S` for this process is :

Options

A. `2C_(p)"In"((T_(1)+T_(2))/(4T_(1)T_(2)))`
B. `2C_(p)"In"[((T_(1)+T_(2))^(1/2))/(T_(1)T_(2))]`
C. `C_(p)"In"[((T_(1)+T_(2))^(2))/(4T_(1)T_(2))]`
D. `2C_(p)"In"[(T_(1)+T_(2))/(2T_(1)T_(2))]`

Answer

C

Explanation

`T_("Final") = (T_1 + T_2)/2`
`DeltaS_(I) = C_P ln (T_f/T_1)`
`DeltaS_(II) = C_P ln(T_f/T_2)`
`DeltaS = Delta S_(I) + DeltaS_(II)`
`=C_P ln(T_f^2/(T_1T_2)) =C_Pln[(((T_1 + T_2)/2)^2)/(T_1T_2)]`