a 35 g ice cube at 0.0 C is added to 110 g of water in a 62 g aluminium cup. The cup and the water have an initial temperature of 23 C . Find the equilibrium temperature of this system? in Celsius ,, I've been trying to solve this for 2 hours now , and I still can't get the answer ,, help please ?
The sum of the heats gained equals zero (yes, the substance losing heat is negative).
sum heats gained=0
35*Hfice+62(Calum)*(Tf-0)+35(Cwater)(Tf-0)+ 110*Cwater(Tf-23)=0
solve for Tf.
Assume all of the ice melts. (If it doesn't you will find out later when you compute the final temperature).
Look up the specific heat of aluminum. It is 0.22 cal/C gm
Assume the heat lost by the water and aluminum when being lowered to final temperature T equals the heat gained by the ice when melting and rising to the same temperature T. Solve for T .
( 110*1.0 + 62*0.22)*(23 - T) = 35*(80 + 1.0*T)
The 1.0 numbers are specific heats of water and 80 cal/g is the latent heat of fusion of ice
If you get a negative T (in C) , all of the ice did not melt.
Thanx I will try it out
To find the equilibrium temperature of the system, we can use the principle of conservation of energy. The total amount of heat lost by the ice cube and gained by the water and the cup must be equal at equilibrium.
Let's calculate the heat lost by the ice cube first. The heat lost (Q1) by the ice cube can be calculated using the formula:
Q1 = mass of the ice cube (m1) * specific heat capacity of ice (c1) * change in temperature (ΔT1)
The mass of the ice cube is given as 35 g, specific heat capacity of ice is 2.09 J/g°C, and the change in temperature is the difference between the initial temperature of the ice cube (0.0°C) and the equilibrium temperature (T, in °C).
Next, let's calculate the heat gained by the water. The heat gained (Q2) by the water can be calculated using the formula:
Q2 = mass of water (m2) * specific heat capacity of water (c2) * change in temperature (ΔT2)
The mass of the water is given as 110 g, the specific heat capacity of water is 4.18 J/g°C, and the change in temperature is the difference between the equilibrium temperature (T) and the initial temperature of the water (23°C).
Lastly, let's calculate the heat gained by the cup. The heat gained (Q3) by the cup can be calculated using the formula:
Q3 = mass of the cup (m3) * specific heat capacity of aluminium (c3) * change in temperature (ΔT3)
The mass of the cup is given as 62 g, the specific heat capacity of aluminium is 0.897 J/g°C, and the change in temperature is the difference between the equilibrium temperature (T) and the initial temperature of the cup (23°C).
Now, at equilibrium, the heat lost by the ice cube (Q1) is equal to the heat gained by the water (Q2) and the cup (Q3).
Q1 = Q2 + Q3
Using the calculated formulas and substituting the given values, we can solve for the equilibrium temperature (T). It's a bit complicated to solve manually, but I can help you with the calculations.