To develop this problem it is necessary to apply the definitions of entropy change within the bodies
The change of entropy in copper would be defined as
[tex]\Delta S= \frac{\delta Q}{T}[/tex]
Where,
Q= Heat exchange
T = Temperature
For an incompressible substance, the change in the heat exchange is defined as
[tex]\Delta Q =mcdT[/tex]
Where,
m = Mass
c = Specific heat
Replacing in our equation we have that
[tex]\Delta S = \frac{mcdT}{T}[/tex]
[tex]\Delta S = mc ln \frac{T_f}{T_i}[/tex]
Since [tex]\Delta S = 0[/tex], then
[tex]mcln\frac{T_f}{T_i} = 0[/tex]
[tex]T_f = T_i[/tex]
In this way for the change of enthalpy and internal energy you have to
[tex]\Delta U = \Delta h = mc\Delta T = mc(T_f-T_i)[/tex]
As [tex]Tf_= T_i[/tex], then
[tex]\Delta U = 0, \Delta H = 0[/tex]
Therefore the correct option is A. No change at All
