Robert Sutherland
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HS1 Physics1
Heat Capacity
Practice Problem
How much energy does it take to boil a 100g ice cube?
(The ice cube starts at 0°C)
l_{fusion} = 0.334\ \dfrac{kJ}{kg}\\
l_{vapor} = 2.260\ \dfrac{kJ}{kg}\\
Q = m \cdot l
c_{ice} = 2.108\ \dfrac{kJ}{kgC}\\
c_{water} = 4.187\ \dfrac{kJ}{kgC}\\
c_{steam} = 1.996\ \dfrac{kJ}{kgC}\\
Q = m \cdot c \Delta T
Practice Problem
l_{fusion} = 0.334\ \dfrac{kJ}{kg}\\
l_{vapor} = 2.260\ \dfrac{kJ}{kg}\\
Q = m \cdot l
c_{ice} = 2.108\ \dfrac{kJ}{kgC}\\
c_{water} = 4.187\ \dfrac{kJ}{kgC}\\
c_{steam} = 1.996\ \dfrac{kJ}{kgC}\\
Q = m \cdot c \Delta T
Q \rightarrow \text{Heat} \\
m \rightarrow \text{mass} \\
l \rightarrow \text{latent heat} \\
c \rightarrow \text{specific heat} \\
\Delta T \rightarrow \text{Change in temperature}
Solid to Liquid
l_{fusion} = 0.334\ \dfrac{kJ}{kg}\\
Q = m \cdot l_{fusion}
①
①
0.1kg ice cube
Q_{s \rightarrow l} = 0.1kg \cdot 0.334\ \dfrac{kJ}{kg} = 0.0334\ kJ
Liquid to Gas
l_{vapor} = 2.260\ \dfrac{kJ}{kg}\\
Q = m \cdot l_{vapor}
①
②
0.1kg of water
Q_{l \rightarrow g} = ①\ +\ ② = 41.87\ kJ + 0.226\ kJ
②
①
c_{water} = 4.187\ \dfrac{kJ}{kg} \\
Q = m \cdot c_{water} \cdot \Delta T
Practice Problem
How much energy does it take to boil a 100g ice cube?
(The ice cube starts at 0°C)
Q_{s \rightarrow l} = 0.211\ kJ
Q_{l \rightarrow g} = 42.096\ kJ
Q = 42.307
Heat Capacity
By Robert Sutherland
