Question

A 41.6 g block of copper whose temperature is 372 K is placed in an insulating box with a 59.3 g block of lead whose temperature is 146 K. (a) What is the equilibrium temperature of the two-block system? (b) What is the change in the internal energy of the two-block system between the initial state and the equilibrium state? (c)What is the change in the entropy of the two-block system? The heat capacities of copper and lead are 386 J/kg·K and 128 J/kg·K, respectively.

Answer 1

We know that through an insulating system, the net heat flow is zero.

Mc Cc (Tf - Tic) + Ml Cl (Tf - Til) = 0

Tf = (Mc Cc Tic + Ml Cl Til)/( Mc Cc + Ml Cl)

Tf = (0.0416*386*372 + 0.0593*128*146)/ (0.0416*386 + 0.0593*128) = 299.5 K

Hence, Tf = 299.5 K

b)The system is thermally insulated and no work work has been done so the change in internal energy is zero.

c)The change in entropy will be given by

delta S(sys) = Sc + Sl

delta S = Mc Cc ln(Tf/Tic) + Ml Cl ln(Tf/Til)

deltaS = 0.0416*386*ln(299.5/372) + 0.0593*128*ln(299.5/146) = 1.9 J/K

Hence, delta S = 1.9 J/K