What is the final temperature when 750 J of energy is added to 9.0 g of ice at 0.0 degress C?
To find the final temperature when energy is added to ice, we need to understand the concept of heat and the specific heat capacity of water and ice.
First, we can write down the equation to calculate the heat transferred:
Q = m * c * ΔT
Where:
Q is the heat transferred
m is the mass of the substance
c is the specific heat capacity
ΔT is the change in temperature
In this case, we want to find the final temperature (ΔT), and we know the following information:
- The energy added to the system is 750 J.
- The mass of the ice is 9.0 g.
- The initial temperature of the ice is 0.0 °C.
To find the final temperature, we need to rearrange the equation to solve for ΔT:
ΔT = Q / (m * c)
Now, let's consider the specific heat capacity of ice and water. The specific heat capacity of ice is approximately 2.09 J/g°C, and the specific heat capacity of water is about 4.18 J/g°C.
Given that ice is undergoing a phase change from solid to liquid, we need to use two parts to calculate the final temperature: one for heating the ice from 0.0 °C to its melting point, and another for melting the ice.
1. Calculate the heat required to raise the temperature of the ice to its melting point (0 °C):
Q1 = m * c_ice * ΔT1
Where:
Q1 is the heat required to raise the temperature of the ice
c_ice is the specific heat capacity of ice (2.09 J/g°C)
ΔT1 is the change in temperature (final temperature - initial temperature)
Since we are dealing with a phase change from solid to liquid, the final temperature (ΔT1) will be the melting point of ice (0 °C). Therefore, the equation simplifies to:
Q1 = m * c_ice * 0
2. Calculate the heat required to melt the ice:
Q2 = m * ΔH_fusion
Where:
Q2 is the heat required to melt the ice
ΔH_fusion is the enthalpy of fusion (heat required to convert 1 gram of ice at its melting point to water at the same temperature) -- for water, it is approximately 334 J/g
Now, we can find the total heat required (Qtotal) to raise the temperature of ice to its melting point and melt the ice:
Qtotal = Q1 + Q2
Finally, we can substitute the given values into the equation to find the final temperature (ΔT2) when 750 J of energy is added to 9.0 g of ice at 0.0 °C:
ΔT2 = Qtotal / (m * c_water)
Where:
ΔT2 is the final temperature
Using the specific heat capacity of water (c_water = 4.18 J/g°C), we can calculate the value of ΔT2.