Published by:
CGP EDU Academic Team
Published on: September 12, 2026
300 g of water at 25ºC is added to 100 g of ice at 0ºC. Find the final temperature of the mixture.
Text Solution
Verified by ExpertsThe correct answer is:
0°C
Step 1: Calculate the heat required to melt the ice.
The heat required to melt ice is given by:
$Q = m_{ice} \cdot L_f$
where $m_{ice} = 100 g$ and $L_f = 334 \frac{kJ}{kg} = 334 \frac{J}{g}$ (latent heat of fusion for ice).
Therefore,
$Q = 100 g \cdot 334 \frac{J}{g} = 33400 J$.
Step 2: Calculate the heat lost by the water when it cools down to 0ºC.
The water will cool from 25ºC to 0ºC, and the heat lost is given by:
$Q = m_{water} \cdot c_{water} \cdot \Delta T$
where $m_{water} = 300 g$, $c_{water} = 4.18 \frac{J}{gºC}$, and $\Delta T = 25ºC - 0ºC = 25ºC$.
Therefore,
$Q = 300 g \cdot 4.18 \frac{J}{gºC} \cdot 25ºC = 31350 J$.
Step 3: Compare the heat required to melt the ice with the heat lost by the water.
The heat lost by water (31350 J) is less than the heat required to melt the ice (33400 J). This means that not all the ice will melt, and the final temperature will be at the melting point of ice (0ºC).
Conclusion: The final temperature of the mixture is 0ºC.
The heat required to melt ice is given by:
$Q = m_{ice} \cdot L_f$
where $m_{ice} = 100 g$ and $L_f = 334 \frac{kJ}{kg} = 334 \frac{J}{g}$ (latent heat of fusion for ice).
Therefore,
$Q = 100 g \cdot 334 \frac{J}{g} = 33400 J$.
Step 2: Calculate the heat lost by the water when it cools down to 0ºC.
The water will cool from 25ºC to 0ºC, and the heat lost is given by:
$Q = m_{water} \cdot c_{water} \cdot \Delta T$
where $m_{water} = 300 g$, $c_{water} = 4.18 \frac{J}{gºC}$, and $\Delta T = 25ºC - 0ºC = 25ºC$.
Therefore,
$Q = 300 g \cdot 4.18 \frac{J}{gºC} \cdot 25ºC = 31350 J$.
Step 3: Compare the heat required to melt the ice with the heat lost by the water.
The heat lost by water (31350 J) is less than the heat required to melt the ice (33400 J). This means that not all the ice will melt, and the final temperature will be at the melting point of ice (0ºC).
Conclusion: The final temperature of the mixture is 0ºC.
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