To calculate the final temperature of the calorimeter and its contents, we need to use the principle of energy conservation. The heat lost by the hot object (steam) is equal to the heat gained by the cooler object (water and calorimeter).
First, let's calculate the heat lost by the steam using the equation:
Heat lost = mass x specific heat x change in temperature
The mass of the steam is given as 100g. The specific heat of steam is not mentioned, but we can assume it to be negligible compared to water, so we can ignore it. The change in temperature of the steam can be calculated as the final temperature of the system minus the initial temperature of the steam (100°C).
Heat lost = 100g x 1 cal/g°C x (final temperature - 100°C) [1 cal = 1 kcal]
Next, let's calculate the heat gained by the water and calorimeter using the equation:
Heat gained = mass x specific heat x change in temperature
The mass of water is given as 1kg (1000g), and the specific heat of water is given as 1 kcal/kg°C. The change in temperature can be calculated as the final temperature of the system minus the initial temperature of the water (20°C).
Heat gained = 1000g x 1 cal/g°C x (final temperature - 20°C)
Since the heat lost by the steam is equal to the heat gained by the water and calorimeter, we can set up the following equation:
Heat lost = Heat gained
100g x 1 cal/g°C x (final temperature - 100°C) = 1000g x 1 cal/g°C x (final temperature - 20°C)
Simplifying the equation:
final temperature - 100°C = 10 x (final temperature - 20°C)
final temperature - 100°C = 10final temperature - 200°C
9final temperature = 100°C
final temperature = 100°C / 9 ≈ 11.11°C
Therefore, the final temperature of the calorimeter and its contents is approximately 11.11°C.