What is the amount of energy required to raise the temperature of a 2.5 kg block of ice at -25°C to steam at 100°C?
To find the amount of energy required to raise the temperature of a substance, you can use the equation:
Q = m * c * ΔT
Where:
Q is the amount of energy (in joules),
m is the mass of the substance (in kg),
c is the specific heat capacity of the substance (in J/kg°C), and
ΔT is the change in temperature (in °C).
In this case, the substance in question goes through three phases: ice, water, and steam. Each phase requires a different amount of energy.
First, we need to calculate the amount of energy required to raise the temperature of the ice from -25°C to its melting point at 0°C. Since ice has a specific heat capacity of 2.09 J/g°C, we need to convert the mass of the block of ice from kg to grams (1 kg = 1000 g):
m_ice = 2.5 kg = 2500 g
ΔT_ice = 0°C - (-25°C) = 25°C
Q_ice = m_ice * c_ice * ΔT_ice
Next, we need to calculate the amount of energy required to melt the ice into water. The heat of fusion for ice is 334 J/g:
Q_fusion = m_ice * ΔH_fusion
Finally, we need to calculate the amount of energy required to raise the temperature of the water from its melting point (0°C) to the boiling point (100°C). The specific heat capacity of water is 4.18 J/g°C:
m_water = m_ice
ΔT_water = 100°C - 0°C = 100°C
Q_water = m_water * c_water * ΔT_water
Now, to calculate the total amount of energy required to go from ice at -25°C to steam at 100°C, we add up the three calculated values:
Total energy = Q_ice + Q_fusion + Q_water
Calculating each of these values and adding them together will give you the final answer.