What is the resulting temperature when a 150g cube of ice at zero degrees celsius is added to 200g of water in a 100g aluminium cup at 30degrees celsius.
Compute the amount of heat necessary to be removed from the Al and liquid H2O to reduce both to 0 C.
If that heat can be absorbed by the melting of less than 150g or less of ice, then the equilibrium temperature is 0 C.
If not, you will have to do some algebra to get the equilibrium temperature, assuming all the ice melts and is heated to the equilibrium temperature.
You will need the latent heat of fusion of ice (80 cal/g) and the specific heat of aluminum (0.213 cal/g*C).
25 degree celsius
To find the resulting temperature when the ice is added to the water in the aluminum cup, we can use the principle of energy conservation.
First, we need to calculate the energy gained or lost by each component: the ice, water, and aluminum cup.
1. Energy gained or lost by ice:
The energy gained or lost by the ice can be calculated using the specific heat capacity formula:
Q = m * c * ΔT,
where Q is the amount of energy gained or lost, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
Since we are starting with ice at 0 degrees Celsius and we want to find the final temperature, we can say ΔT = Tf - 0, where Tf is the final temperature.
The specific heat capacity of ice is 2.09 J/g°C.
So, for the ice, the energy gained or lost is Q = 150g * 2.09 J/g°C * (Tf - 0).
2. Energy gained or lost by water:
Similarly, for the water, the energy gained or lost is Q = 200g * 4.18 J/g°C * (Tf - 30).
The specific heat capacity of water is 4.18 J/g°C.
3. Energy gained or lost by the aluminum cup:
For the aluminum cup, the energy gained or lost can be calculated using the formula:
Q = m * c * ΔT,
where m is the mass of the cup and c is the specific heat capacity of aluminum. The change in temperature is Tf - 30, as the initial temperature of the cup is 30 degrees Celsius.
The specific heat capacity of aluminum is 0.897 J/g°C.
So, for the aluminum cup, the energy gained or lost is Q = 100g * 0.897 J/g°C * (Tf - 30).
Now, since energy is conserved, the energy gained by the ice and water must be equal to the energy lost by the aluminum cup. Therefore, we can set up an equation:
150g * 2.09 J/g°C * (Tf - 0) + 200g * 4.18 J/g°C * (Tf - 30) = 100g * 0.897 J/g°C * (Tf - 30)
Now, solve this equation to find the value of Tf, which represents the resulting temperature.