Question

What weight of ice could be melted at \(0^{\circ} \mathrm{C}\) by the heat liberated by condensing \(100 \mathrm{~g}\) of steam at \(100^{\circ} \mathrm{C}\) to liquid. Heat of vaporization \(=540 \mathrm{cal} / \mathrm{g}\), heat of fusion \(=80 \mathrm{cal} / \mathrm{g}\).

Short answer

The weight of ice that can be melted by the heat liberated by condensing 100 g of steam at 100 degrees Celsius to liquid is \(675 \mathrm{g}\).

Step-by-step solution

Calculate the total heat energy released by the steam

The total heat energy released by the steam during the condensation process can be calculated using the formula: Heat energy released = (Mass of steam) × (Heat of vaporization) We're given the mass of the steam as 100 g and the heat of vaporization as 540 cal/g. Plugging these values into the formula, we get: Heat energy released = (100 g) × (540 cal/g) = 54000 cal

Determine the amount of heat required to melt the ice

To melt the ice, we need to use the heat of fusion. The formula for the heat required to melt the ice is: Heat required = (Mass of ice) × (Heat of fusion) We're given the heat of fusion as 80 cal/g. We need to find the mass of ice, so we'll rearrange the formula to solve for the mass of ice: Mass of ice = Heat required / Heat of fusion

Calculate the weight of ice that can be melted by the heat liberated from the steam

We now have the total heat energy released by the steam (54000 cal) and the heat required to melt the ice (80 cal/g). We can use these values to find the mass of ice that can be melted: Mass of ice = 54000 cal / 80cal/g = 675 g The weight of ice that can be melted by the heat liberated by condensing 100 g of steam at 100 degrees Celsius to liquid is 675 g.

Key concepts

Enthalpy of Vaporization

Enthalpy of vaporization is a term used in thermodynamics to describe the amount of energy required to convert a substance from a liquid to a gaseous state at constant pressure. It is a type of latent heat, latent because it is the energy provided to the substance without a change in temperature during the phase transition. For instance, the enthalpy of vaporization for water is typically around 540 calories per gram. This value is significant, as it represents the energy needed to break the intermolecular forces that hold the liquid molecules together.

In a practical sense, when steam condenses back into water, it releases this stored energy, which can be transferred to other substances, such as ice in our example. The release of this energy can be used to calculate the heat exchange in processes involving phase changes from gas to liquid, impacting fields such as meteorology, engineering, and understanding of natural processes.

Enthalpy of Fusion

Enthalpy of fusion, also recognized as the heat of fusion, is the energy required for changing a substance from solid to liquid at its melting point. Similar to vaporization, the phase change occurs at a constant temperature and the energy alters the structure of the substance instead of raising its temperature. For ice, the typical value of the heat of fusion is approximately 80 calories per gram.

This physical quantity is essential in calculating the amount of heat needed to melt a solid without increasing its temperature. During melting, this energy is absorbed to overcome the forces keeping the solid structure intact. Conversely, during freezing, the same amount of energy is released. Understanding the enthalpy of fusion is crucial in various applications, such as the design of heat-exchange systems, determining energy requirements in industrial processes, and even in calculating the amount of ice that can be melted by a given amount of heat, as demonstrated in the exercise.

Phase Change

A phase change is a transition of matter from one state to another, typically between solid, liquid, and gaseous phases. This concept is rooted in the understanding that matter can exist in different states depending on temperature and pressure conditions. Phase changes include melting, freezing, vaporization, condensation, sublimation, and deposition.

During phase changes, substances absorb or release energy, but their temperature remains constant. Heat energy alters the physical arrangement of molecules within a substance without increasing the kinetic energy that would otherwise raise the temperature. The ability to predict and quantify the energy involved in phase transitions is of fundamental importance in sciences such as physics, chemistry, and environmental science. Analyzing phase changes provides insight into energy transfer processes and helps in designing systems that utilize these changes effectively, as seen in our exercise with the melting of ice and condensation of steam.

Thermochemistry

Thermochemistry is the branch of chemistry that deals with the energy changes during chemical and physical transformations. Key concepts include enthalpy changes, heat of reaction, and calorimetry. These principles allow for understanding how energy is absorbed or released in chemical processes, as well as phase changes.

Calculations in thermochemistry involve assessing these energy exchanges, often using values such as enthalpy of vaporization and fusion. In practical applications, thermochemistry is used to measure the energy efficiency of reactions, determine heat balances, and optimize industrial processes for energy conservation. Gaining a deep understanding of thermochemistry is useful for fields ranging from materials science to environmental sustainability, and it connects directly to exercises like the one given, where we're required to perform heat transfer calculations based on known thermochemical properties.