Answer:
To calculate AE and AH when the temperature of water is increased from 10°C to 70°C, we can use the formula:
AE = m × c × ΔT
Where:
- AE is the change in internal energy
- m is the mass of water
- c is the specific heat capacity of water
- ΔT is the change in temperature
First, we need to calculate the mass of water. We know that the density of water is 0.9997 g/cm³ at 10°C and 0.9778 g/cm³ at 70°C. Since the density is mass divided by volume, we can rearrange the formula to solve for mass:
mass = density × volume
We can assume the volume of water remains constant. Therefore, the mass at 10°C is:
mass₁ = density₁ × volume
And the mass at 70°C is:
mass₂ = density₂ × volume
Now, we need to calculate the specific heat capacity of water. The specific heat capacity of water is approximately 4.18 J/g°C.
Using the given values, we can calculate the change in internal energy:
AE = (mass₂ × c × (70°C - 10°C)) - (mass₁ × c × (70°C - 10°C))
Finally, to calculate AH (the enthalpy change), we need to consider any phase changes that occur. Water undergoes a phase change from liquid to gas at 100°C. If the final temperature is below 100°C, there is no phase change and AH is equal to AE. However, if the final temperature is above 100°C, we need to consider the energy required for the phase change.
In this case, since the final temperature is 70°C, AH is equal to AE.