Problem 145 - Master Resource Book in JEE Main Physics

Question

Heat released when \(10 \mathrm{~g}\) of steam at \(100^{\circ} \mathrm{C}\) cools to water at \(100^{\circ} \mathrm{C}\) is (a) \(540 \mathrm{cal}\) (b) \(54 \mathrm{cal}\) (c) \(5400 \mathrm{cal}\) (d) \(54000 \mathrm{cal}\)

Step-by-Step Solution

Answer

The heat released is 5400 cal (option c).

Step 1: Understand the process

We need to find the heat released when steam at 100°C condenses to liquid water at the same temperature. The process involved is condensation, which is the phase change of steam (gas) to water (liquid).

Step 2: Identify the heat of condensation

The latent heat of vaporization (or condensation) of water is approximately 540 cal/g. This is the amount of heat released when 1 gram of steam condenses at 100°C.

Step 3: Calculate total heat released

To find the total heat released, multiply the mass of the steam by the heat of condensation: \[ Q = m \times L \]where \( m = 10 \text{ g} \) and \( L = 540 \text{ cal/g} \).

Step 4: Perform the calculation

Substitute the values into the formula: \[ Q = 10 \times 540 = 5400 \text{ cal} \]

Step 5: Analyze the result

The calculated heat released is 5400 cal, which matches one of the given answer choices.

Key Concepts

Phase Change

Phase change is the process of transforming a substance from one state of matter to another. This typically involves transitioning between solid, liquid, and gas. During a phase change, the temperature of the system remains constant as the substance absorbs or releases energy. The key aspects of a phase change include:

• Temperature Stability: While the phase change occurs, the temperature doesn't change until the entire substance has transformed into a new state.
• Latent Heat: This is the energy absorbed or released during the phase change. For instances like steam condensing to water, latent heat is released.

Understanding phase change helps in grasping the energy dynamics when substances interact, such as in steam condensing to water.

Condensation

Condensation is a specific type of phase change where a gas turns into a liquid. This occurs when the gas cools down, and molecules lose kinetic energy, moving closer together. Important points about condensation include:

• Energy Release: When gas condenses, latent heat of vaporization is released. For water, this value is approximately 540 cal/g.
• Everyday Phenomena: Condensation is common in daily life, such as dew forming on grass or water droplets on a cold glass.

By understanding condensation, students can see why energy is released during the cooling of steam into water.

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. In the context of condensation, it helps calculate the heat released when steam turns to water. Key concepts of calorimetry include:

• Calorimeter Use: An instrument called a calorimeter is used to measure heat exchange.
• Measurement Formula: Calorimetry relies on formulas like \( Q = m \times L \), where \( Q \) is the heat exchanged, \( m \) is the mass, and \( L \) is the latent heat value.
• Applications: Besides phase changes, it measures heat in chemical reactions, helping scientists understand energy changes.

Calorimetry equips learners with the tools to quantify heat transfer during phase changes like condensation.

Heat Transfer

Heat transfer involves the movement of thermal energy from one object or substance to another. It can occur through conduction, convection, or radiation. In the context of steam condensing into water, heat transfer is crucial:

• Conduction: Direct heat transfer through material contacts. Often less significant in the case of water vapor but crucial in solid-liquid interactions.
• Convection: The transfer of heat by the movement of fluids. This is often observed in boiling or cooling processes.
• Total Heat Release: The concept of total heat, where the whole amount released during condensation is calculated by multiplying the mass by the latent heat of vaporization.

Knowing how heat transfer works helps students understand how energy moves and changes form during condensation and other phase changes.