A cubical vessel of side 10 cm is filled with ice at 0 degree cel …. Ans 12 sec

To determine how long it takes for the ice in a cubical vessel to melt, we need to consider several factors, including the properties of the ice, the heat transfer involved, and the specific conditions of the environment. Let's break this down step by step.

Understanding the Scenario

We have a cubical vessel with a side length of 10 cm, which means the volume of the cube is:

• Volume = side³ = 10 cm × 10 cm × 10 cm = 1000 cm³

This volume corresponds to 1 liter of ice, which weighs approximately 1 kg since the density of ice is about 0.92 g/cm³. For our calculations, we will consider the mass of the ice to be 1 kg.

Melting Ice: The Basics

Ice melts at 0 degrees Celsius, and to melt ice, we need to supply heat. The amount of heat required to melt ice can be calculated using the formula:

• Q = m × Lf

Where:

• Q = heat required (in joules)
• m = mass of the ice (in kg)
• Lf = latent heat of fusion of ice (approximately 334,000 J/kg)

For our 1 kg of ice, the heat required to melt it is:

• Q = 1 kg × 334,000 J/kg = 334,000 J

Heat Transfer Considerations

Next, we need to consider how heat is transferred to the ice. This can occur through conduction, convection, or radiation, depending on the environment. For simplicity, let’s assume the ice is in a room at a temperature significantly above 0 degrees Celsius, and heat is being transferred primarily through convection from the surrounding air.

Calculating the Rate of Heat Transfer

The rate of heat transfer can be estimated using Newton's Law of Cooling, which states:

• Q/t = h × A × (T - T_ice)

Where:

• Q/t = rate of heat transfer (in watts)
• h = heat transfer coefficient (typically around 10-100 W/m²K for air)
• A = surface area of the ice (in m²)
• T = temperature of the surrounding air (in °C)
• T_ice = temperature of the ice (0 °C)

The surface area of the ice can be calculated as follows:

• Surface Area = 6 × (side²) = 6 × (0.1 m)² = 0.06 m²

Putting It All Together

Assuming a heat transfer coefficient of about 25 W/m²K (a reasonable estimate for air), and if we consider the surrounding air to be at 20 °C, we can calculate the rate of heat transfer:

• Q/t = 25 W/m²K × 0.06 m² × (20 °C - 0 °C) = 30 W

Now, we can find the time it takes to supply the required heat to melt the ice:

• t = Q / (Q/t) = 334,000 J / 30 W ≈ 11,133 seconds

This is approximately 3.1 hours, which is significantly longer than 12 seconds. Therefore, if the answer provided is indeed 12 seconds, it might refer to a different scenario or specific conditions not mentioned in the question.

Final Thoughts

In real-world applications, the time it takes for ice to melt can vary greatly based on environmental conditions, the size of the ice, and the method of heat transfer. Always consider these factors when analyzing similar problems.