An ice cube at 0°C measures 13.9 cm on a side. It sits on top of a copper block with a square cross section 13.9 cm on a side and a length of 19.1 cm. The block is partially immersed in a large pool of water at 88.5°C. How long does it take the ice cube to melt? Assume that only the part in contact with the copper liquefies; that is, the cube gets shorter as it melts. The density of ice is 0.917 g/cm3.

Question

An ice cube at 0°C measures 13.9 cm on a side. It sits on top of a copper block with a square cross section 13.9 cm on a side and a length of 19.1 cm. The block is partially immersed in a large pool of water at 88.5°C. How long does it take the ice cube to melt? Assume that only the part in contact with the copper liquefies; that is, the cube gets shorter as it melts. The density of ice is 0.917 g/cm3.

Answer 1

A copper cube has dimensions 5cm x4cm x3cm what is the massof this cube

Answer 2

To determine how long it takes for the ice cube to melt, we need to calculate the amount of heat transferred from the water to the ice cube and then divide it by the heat required to melt the ice.

Here's a step-by-step approach to solve the problem:

Step 1: Calculate the mass of the ice cube.
The ice cube has a length, width, and height of 13.9 cm each. The density of ice is given as 0.917 g/cm^3. Therefore, the volume of the ice cube is (13.9 cm)^3. The mass of the ice cube can be calculated by multiplying the volume by the density.

Step 2: Calculate the heat transferred from the water to the ice cube.
The heat transferred (Q) can be calculated using the formula Q = mcΔT, where:
- m is the mass of the ice cube.
- c is the specific heat capacity of water, which is approximately 4.18 J/g°C.
- ΔT is the change in temperature, which is the difference between the temperature of the water and the melting point of ice.

Step 3: Calculate the heat required to melt the ice.
The heat required to melt the ice (Q_melting) can be calculated using the formula Q_melting = mL, where:
- m is the mass of the ice cube.
- L is the heat of fusion of ice, which is approximately 334 J/g.

Step 4: Determine the time it takes for the ice cube to melt.
To find the time, divide the heat required to melt the ice by the heat transferred per unit of time.

Now, let's calculate each step:

Step 1:
The volume of the ice cube = (13.9 cm)^3 = 2677.03 cm^3
The mass of the ice cube = volume x density = 2677.03 cm^3 x 0.917 g/cm^3 = 2454.05 g

Step 2:
ΔT = temperature of water - melting point of ice = 88.5°C - 0°C = 88.5°C
Q = mcΔT = 2454.05 g x 4.18 J/g°C x 88.5°C = 930730.383 J

Step 3:
Q_melting = mL = 2454.05 g x 334 J/g = 819046.7 J

Step 4:
Time = Q_melting / Q = 819046.7 J / 930730.383 J = 0.88 hours

Therefore, it takes approximately 0.88 hours (or 52.8 minutes) for the ice cube to melt.