STEM Problem Detail

Problem Statement

Prompt

Give me the solution of the question 15

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## Solutions 15

Initial: $$m_w = 1773\ \text{g}$$ water, $$m_i = 227\ \text{g}$$ ice at $$0.000^\circ\mathrm{C}$$.
Final: water–ice mass ratio 1.00:1.00 at $$0.000^\circ\mathrm{C}$$.
Total mass = $$1773 + 227 = 2000\ \text{g}$$.
Final: $$m_w' = 1000\ \text{g}$$, $$m_i' = 1000\ \text{g}$$.
So $$1000 - 1773 = -773\ \text{g}$$ water changed to ice? Wait, initial water=1773, final water=1000, so water decreased by 773 g, meaning 773 g water froze.

(a) Reversible process at $$T=273\ \text{K}$$.
Heat removed: $$Q = m L_f = 0.773\ \text{kg} \times 333\ \text{kJ/kg} = 257.3\ \text{kJ}$$ (negative since leaving system).
Entropy change of system: $$\Delta S = -\frac{Q}{T} = -\frac{257.3 \times 10^3}{273} \approx -942.5\ \text{J/K}$$.

(b) Irreversible process back to initial state: entropy change of system = $$+942.5\ \text{J/K}$$ (since entropy increases in irreversible process returning to same state).

(c) Yes: reversible process $$\Delta S_{\text{univ}}=0$$, irreversible $$\Delta S_{\text{univ}}>0$$.

\[
\boxed{(a)\ -943\ \text{J/K}} \quad \boxed{(b)\ 943\ \text{J/K}} \quad \boxed{(c)\ \text{yes}}
\]

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Problem #19