25) A 75-g ice cube at 0 C is placed in 825g of water at 25 C. a) What is the final temperature of the mixture? b) If the final temperature is 0 C, then how much ice remains?
c) change the ice's mass to 300g, and repeat the problem
Let me know what you are having difficulty with.
Calculating Final temperature. I was absent one day from class and didn't get the notes. So I am confused and this Hw is due in less than an hour!
To solve this problem, we need to apply the principles of heat transfer and phase change. We can use the equation:
Q = m * c * ΔT
Where:
- Q is the heat transferred (in calories or joules)
- m is the mass of the substance
- c is the specific heat capacity of the substance
- ΔT is the change in temperature of the substance
a) Final temperature of the mixture:
To find the final temperature of the mixture, we need to find the heat gained by the water and the ice cube separately, and then equate them.
Heat gained by the water:
Q_water = m_water * c_water * ΔT
Where:
- m_water is the mass of water (825 g)
- c_water is the specific heat capacity of water (1 cal/g°C or 4.184 J/g°C)
- ΔT is the change in temperature of water (final temperature - initial temperature)
- Initial temperature of water = 25°C
Heat gained by the ice cube:
Q_ice = m_ice * c_ice * ΔT
Where:
- m_ice is the mass of ice (75 g or 300 g in part c)
- c_ice is the specific heat capacity of ice (0.5 cal/g°C or 2.09 J/g°C)
- ΔT is the change in temperature of ice (final temperature - initial temperature)
- Initial temperature of ice = 0°C
Since the final temperature of the mixture will be the same for both substances, we can equate the two heat gained equations:
Q_water = Q_ice
m_water * c_water * ΔT_water = m_ice * c_ice * ΔT_ice
To solve for the final temperature, we rearrange the equation:
(final temperature - 25) = (m_ice * c_ice * ΔT_ice) / (m_water * c_water)
b) Amount of ice remaining if final temperature is 0°C:
If the final temperature is 0°C, then all the ice has melted. Therefore, no ice will remain.
c) Changing the ice's mass to 300g and repeating the problem:
To repeat the problem with a different ice mass, substitute the new value of m_ice (300 g) into the equations given in part a. Re-calculate the final temperature and the amount of ice remaining using the new values.