Physics

Problem

Two

1.0\,\text{kg}

aluminum blocks, each with specific heat capacity

c=900\,\text{J}\,\text{kg}^{-1}\,\text{K}^{-1}

, are placed in thermal contact inside an insulated container. Block A is initially at

400\,\text{K}

and block B at

300\,\text{K}

. They eventually reach the common temperature

350\,\text{K}

. Which of the following is closest to the total change in entropy

\Delta S_{\text{total}}

of the two-block system? a)

0\,\text{J}\,\text{K}^{-1}

+9\,\text{J}\,\text{K}^{-1}

+18\,\text{J}\,\text{K}^{-1}

-18\,\text{J}\,\text{K}^{-1}

Intuitive explanation

This is a problem about entropy change during irreversible heat transfer—the key is that heat flows from hot to cold, increasing disorder overall even though energy is conserved. You'll calculate the entropy change for each block separately using $\Delta S = mc\ln(T_f/T_i)$ , then add them together; the crucial insight is that the block losing heat (A) has a smaller entropy decrease than the block gaining heat (B) has an entropy increase, so the total entropy rises, reflecting the irreversibility of the process.

Intuitive explanation

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