Question:
The amount of heat needed to heat \(200\,\text{g}\) of ice at \(-10^\circ\text{C}\) to convert it into water at \(30^\circ\text{C}\) is:
\[
\text{Specific heat capacity of ice}=2100\,\text{J kg}^{-1}\text{K}^{-1}
\]
\[
\text{Specific heat capacity of water}=4186\,\text{J kg}^{-1}\text{K}^{-1}
\]
\[
\text{Latent heat of fusion of ice}=3.35\times10^5\,\text{J kg}^{-1}
\]
The amount of heat needed to heat \(200\,\text{g}\) of ice at \(-10^\circ\text{C}\) to convert it into water at \(30^\circ\text{C}\) is:
\[ \text{Specific heat capacity of ice}=2100\,\text{J kg}^{-1}\text{K}^{-1} \] \[ \text{Specific heat capacity of water}=4186\,\text{J kg}^{-1}\text{K}^{-1} \] \[ \text{Latent heat of fusion of ice}=3.35\times10^5\,\text{J kg}^{-1} \]
\[ \text{Specific heat capacity of ice}=2100\,\text{J kg}^{-1}\text{K}^{-1} \] \[ \text{Specific heat capacity of water}=4186\,\text{J kg}^{-1}\text{K}^{-1} \] \[ \text{Latent heat of fusion of ice}=3.35\times10^5\,\text{J kg}^{-1} \]
Show Hint
For phase change problems, divide the process into stages:
\[
\text{Heating} \rightarrow \text{Melting} \rightarrow \text{Heating again}.
\]
Apply the correct formula separately for each stage.
Updated On: Jun 24, 2026
- \(96316\,\text{J}\)
- \(67000\,\text{J}\)
- \(92116\,\text{J}\)
- \(71200\,\text{J}\)
Show Solution
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The Correct Option is A
Solution and Explanation
Step 1: Convert the given mass into SI unit.
Given, \[ m=200\,\text{g}=0.2\,\text{kg} \] The process occurs in three stages: \[ \text{(i) Heating ice from }-10^\circ\text{C to }0^\circ\text{C} \] \[ \text{(ii) Melting the ice at }0^\circ\text{C} \] \[ \text{(iii) Heating water from }0^\circ\text{C to }30^\circ\text{C} \]
Step 2: Heat required to raise temperature of ice.
Using \[ Q_1=mc_{\text{ice}}\Delta T \] \[ Q_1=0.2\times2100\times10 \] \[ Q_1=4200\,\text{J} \]
Step 3: Heat required to melt the ice.
Using \[ Q_2=mL \] \[ Q_2=0.2\times3.35\times10^5 \] \[ Q_2=67000\,\text{J} \]
Step 4: Heat required to raise temperature of water.
Using \[ Q_3=mc_{\text{water}}\Delta T \] \[ Q_3=0.2\times4186\times30 \] \[ Q_3=25116\,\text{J} \]
Step 5: Find the total heat required.
\[ Q=Q_1+Q_2+Q_3 \] \[ Q=4200+67000+25116 \] \[ Q=96316\,\text{J} \]
Step 6: Final conclusion.
Hence, the required amount of heat is \[ \boxed{96316\,\text{J}} \]
Given, \[ m=200\,\text{g}=0.2\,\text{kg} \] The process occurs in three stages: \[ \text{(i) Heating ice from }-10^\circ\text{C to }0^\circ\text{C} \] \[ \text{(ii) Melting the ice at }0^\circ\text{C} \] \[ \text{(iii) Heating water from }0^\circ\text{C to }30^\circ\text{C} \]
Step 2: Heat required to raise temperature of ice.
Using \[ Q_1=mc_{\text{ice}}\Delta T \] \[ Q_1=0.2\times2100\times10 \] \[ Q_1=4200\,\text{J} \]
Step 3: Heat required to melt the ice.
Using \[ Q_2=mL \] \[ Q_2=0.2\times3.35\times10^5 \] \[ Q_2=67000\,\text{J} \]
Step 4: Heat required to raise temperature of water.
Using \[ Q_3=mc_{\text{water}}\Delta T \] \[ Q_3=0.2\times4186\times30 \] \[ Q_3=25116\,\text{J} \]
Step 5: Find the total heat required.
\[ Q=Q_1+Q_2+Q_3 \] \[ Q=4200+67000+25116 \] \[ Q=96316\,\text{J} \]
Step 6: Final conclusion.
Hence, the required amount of heat is \[ \boxed{96316\,\text{J}} \]
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