Answered: Suppose you have an ice cube that has a…

Related questions

Question

Suppose you have an ice cube that has a mass of 11.58g at a temperature of -2.8°C. If you add this ice to 71.49g of insulated water at a temperature of 59°C, what is the final temperature of the mixture in °C?

Expert Solution

Step 1

Absorbing the heat from the hot water, the temperature of the ice will first increase to $0^{\circ} C$ , then it will change its state from solid to liquid and then again the temperature of the icy water will increase to the final equilibrium temperature. On the other hand, the hot water release the heat to reach to the final equilibrium temperature.

The amount of heat absorbed by the ice to change its temperature form $- 2 . 8^{\circ} C$ to $0^{\circ} C$ can be written as

$Q_{1} = m_{i} s_{i} (T_{f} - T_{i}) . . . . . . . . . . . . . . . . . (1)$

Here, $Q_{1}$ is the absorbed heat to change the temperature, $m_{i}$ is the mass, $s_{i}$ is the specific heat, $T_{f}$ is the melting point and $T_{i}$ is the initial temperature of the ice.

The amount of heat absorbed by the ice to change its state from solid to liquid can be written as

$Q_{2} = m_{i} L_{i} . . . . . . . . . . . . . . . . . . . . . (2)$

Here, $Q_{2}$ is the heat absorbed by the ice to change its state and $L_{i}$ is the latent heat of fusion.

The amount of heat absorbed by the ice to reach the equilibrium temperature can be written as

$Q_{3} = m_{i} s_{w} (T - T_{f}) . . . . . . . . . . . . . . . . . . . . . . . . (3)$

Here, $Q_{3}$ is the heat absorbed by the icy water at freezing point $T_{f}$ to reach the equilibrium temperature, $s_{w}$ is the specific heat of water and $T$ is the equilibrium temperature.

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here