A 29 g ice cube at 0.0°C is added to 110 g of water in a 62 g iron cup. The cup and the water have an initial temperature of 25°C.
(a) Find the equilibrium temperature of the cup and its contents.
i don't understand how the iron cup changes the situation. please help.
The specific heat of iron is 0.449 J/g K.
It will provide some of the heat needed to melt the ice. The temperature drop of the mixture will be less because the iron is there.
shut up
The iron cup in this situation plays a role in determining the equilibrium temperature because it has a higher thermal conductivity compared to the water. Thermal conductivity refers to the ability of a material to conduct heat. Metal, such as iron, has a high thermal conductivity while liquids like water have lower thermal conductivity.
When the ice cube is added to the water in the cup, heat is transferred between the ice cube, the water, and the cup until they reach a common temperature, known as the equilibrium temperature. The transfer of heat occurs due to the temperature difference between the objects.
Initially, the ice cube is at 0.0°C and the water in the cup is at 25°C. The iron cup also starts at 25°C. Heat is transferred from the water and the cup to the ice cube to melt it, and the final temperature will depend on this heat transfer process.
To find the equilibrium temperature, we need to calculate the heat gained by the ice cube and the heat lost by the water and the cup. This can be done using the specific heat capacity and mass of each substance involved.
The specific heat capacity (C) represents the amount of heat required to raise the temperature of a substance by 1 degree Celsius. The equation used to calculate the heat transfer is:
Q = mcΔT
Where:
- Q is the heat transferred (in joules)
- m is the mass of the substance (in grams)
- c is the specific heat capacity of the substance (in J/g°C)
- ΔT is the change in temperature (in °C)
Since we are assuming no phase change occurs for the water and the cup, we can use the equation:
Qwater = Cwater * mwater * ΔTwater
Qcup = Ccup * mcup * ΔTcup
To find the equilibrium temperature, we set Qwater + Qcup = Qice, where Qice is the heat gained by the ice cube during melting.
Once we have the value of Qice, we can use it to find the final temperature by rearranging the equation:
Qice = mice * Cice * ΔTice
Rearranging this equation, we get:
ΔTice = Qice / (mice * Cice)
Finally, we can calculate the equilibrium temperature by subtracting ΔTice from the initial temperature of the ice cube:
Teq = 0.0°C - ΔTice
By plugging in the given values for the mass, specific heat capacities, and initial temperatures, you can calculate the equilibrium temperature of the cup and its contents.