Question

If 1.10 g of steam at 100.0 °C condenses into 38.5 g of water, initially at 27.0 °C, in an insulated container, what is the final temperature of the entire water sample? Assume no heat is lost to the surroundings.

Answer 1

Answer:

Temperature = 44.02°C

Explanation:

Insulated container indicates no heat loss to the surroundings.

The specific heat capacity of a substance is a physical property of matter. It is defined as the amount of heat that is to be supplied to a unit mass of the material to produce a unit change in its temperature.

The SI unit of specific heat is joule per kelvin and kilogram, J/(K kg).

Now,

Specific heat for water is 4.1813 Jg⁻¹K⁻¹.

Latent heat of vaporization of water is 2257 Jg⁻¹.

Energy lost by steam in it's process of conversion to water, is the energy acquired by water resulting in an increase in it's temperature.

$Q = mS \Delta T$

Q= Heat transferred

m= mass of the substance

T= temperature

Also,

$Q = mL$

L= Latent heat of fusion/ vaporization ( during phase change)

Now applying the above equations to the problem:

$m_{w} S_{w} (T-27) = (m_{s} L) + m_{s}S_{w} (100 -T)$

$38.5 \times 4.1813 \times (T-27) = (1.10 \times 2257) + 1.10 \times 4.1813 \times (100 -T)$

Temperature = 44.02°C