Cooling the Steam

What mass of steam initially at 130^oC is needed to warm 200 g of water in a 100-g glass container from 21.0^oC to 47.0^oC?

Conceptualize Imagine placing water and steam together in a closed insulated container. The system eventually reaches a uniform state of water with a final temperature of 47.0^oC.

Categorize Based on our conceptualization of this situation, we categorize this example as one involving calorimetry in which a phase change occurs. The calorimeter is an isolated system for energy: energy transfers between the components of the system but does not cross the boundary between the system and the environment.

Write an equation to describe the calorimetry process:

The steam undergoes three processes: a decrease in temperature to 100^oC, condensation into liquid water, and finally a decrease in temperature of the water to 47.0^oC. Find the energy transfer in the first process using the unknown mass m_s of the steam:

Find the energy transfer in the second process:

Find the energy transfer in the third process:

Add the energy transfers in these three stages:

The 21.0^oC water and the glass undergo only one process, an increase in temperature to 47.0^oC. Find the energy transfer in this process.