A 100g sample of steam at 100°C is passed into 500g of water at 20°C. Calculate the final temperature of the mixture. (Specific heat capacity of water = 4200 J/kg K, Latent heat of vaporization of ste

Heat lost by steam = Heat gained by water.
We need to consider two phases for the steam: condensation and cooling of the condensed water.
Let $T_f$ be the final temperature.

The initial temperature of water is $20^\circ\text{C}$. If the final temperature is $100^\circ\text{C}$, the change in temperature for water is $\Delta T_w = 100^\circ\text{C} - 20^\circ\text{C} = 80^\circ\text{C}$.
Given:

• Mass of water ($m_w$) = $500 \text{ g} = 0.5 \text{ kg}$
• Specific heat capacity of water ($c_w$) = $4200 \text{ J/kg K}$

Heat gained by water ($Q_{gained, water}$) to reach $100^\circ\text{C}$:

This involves two parts:

• Heat lost by condensation of steam at $100^\circ\text{C}$ to water at $100^\circ\text{C}$ ($Q_{condense}$).
• Heat lost by the condensed water (originally steam) from $100^\circ\text{C}$ to $20^\circ\text{C}$ ($Q_{cool, steam}$).

Given:

• Mass of steam ($m_s$) = $100 \text{ g} = 0.1 \text{ kg}$
• Latent heat of vaporization ($L_v$) = $2.26 \times 10^6 \text{ J/kg}$

Heat lost by condensation:

The heat released by just the condensation of all the steam ($226000 \text{ J}$) is greater than the heat required to raise the temperature of the water to $100^\circ\text{C}$ ($168000 \text{ J}$).
This means that the water will reach $100^\circ\text{C}$, and not all the steam will condense. The excess heat from the steam (if it were to cool further) is not absorbed by the water because the water itself reaches the boiling point of the steam. Therefore, the final temperature of the mixture will be $100^\circ\text{C}$.

To confirm, the mass of steam required to condense to bring the water to $100^\circ\text{C}$ is:

Since $74.3 \text{ g}$ is less than the available $100 \text{ g}$ of steam, the water will reach $100^\circ\text{C}$, and some steam will remain uncondensed at $100^\circ\text{C}$.

The correct option is C.

27.
Good insulators are materials that trap air, which is a poor conductor. Air is an excellent thermal insulator because its molecules are far apart, reducing the frequency of collisions needed for heat transfer by conduction. Many insulating materials, like fiberglass, foam, or wool, work by trapping pockets of air.

The correct option is B.