Question

10 g of steam at the boiling point are combined with 50 g of ice at the freezing point. What is the final temperature of the system?

Accepted Answer

Step 1: Identify the key concepts involved in the problem. This problem involves phase changes (condensation of steam and melting of ice) and heat transfer. The steam will release heat as it condenses and cools, while the ice will absorb heat as it melts and warms. The final temperature will depend on the balance of heat transfer. Step 2: Write the heat transfer equations for each phase change and temperature change. For the steam: the heat released during condensation is given by $$ Q_{condensation} = m_{steam} \cdot L_{v} $$, where $$ L_{v}  is $$the latent heat of vaporization. If the steam cools further, the heat released is $$ Q_{cooling} = m_{steam} \cdot c_{water} \cdot \Delta T . $$For the ice: the heat absorbed during melting is $$ Q_{melting} = m_{ice} \cdot L_{f} $$, where $$ L_{f}  is $$the latent heat of fusion. If the melted ice warms further, the heat absorbed is $$ Q_{warming} = m_{water} \cdot c_{water} \cdot \Delta T . $$Step 3: Set up the heat balance equation. The heat released by the steam must equal the heat absorbed by the ice and water. This can be expressed as $$ Q_{condensation} + Q_{cooling} = Q_{melting} + Q_{warming} . $$Substitute the expressions for $$ Q_{condensation} $$, $$ Q_{cooling} $$, $$ Q_{melting} $$, and $$ Q_{warming} $$ into this equation. Step 4: Solve for the final temperature $$ T_{final} . $$Depending on the amount of heat released and absorbed, the final temperature may be above freezing (if all the ice melts and the water warms) or at freezing (if not all the ice melts). Use the heat balance equation to determine $$ T_{final} . $$Step 5: Check the conditions for phase changes. Ensure that the heat released by the steam is sufficient to melt all the ice and warm the resulting water. If not, adjust the calculations to account for partial melting or cooling of the steam. Use the specific values for $$ L_{v} $$, $$ L_{f} $$, and $$ c_{water}  to $$complete the calculations.

10 g of steam at the boiling point are combined with 50 g of ice at the freezing point. What is the final temperature of the system?

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Key Concepts

Phase Change

Heat Transfer

Specific Heat Capacity