what is the final temperature of mixture, if 100gm of ice at 0 degree celcius into 100gm of water at 20 degree celcius in an iron vessel of mass 100gm.(specific heat of iron=0.1)

To find the final temperature of the mixture, we can use the principle of heat transfer, which states that the total heat gained by one substance is equal to the total heat lost by the other substance during the mixing process.

Let's break down the steps to solve this problem:

1. Calculate the heat gained by the ice:
Heat gained = mass of ice * specific heat of ice * change in temperature
The mass of ice is 100g, the specific heat of ice is 2.09 J/g°C, and the change in temperature is the final temperature minus the initial temperature of the ice. Since the ice is at 0°C initially, the change in temperature is simply the final temperature.
So, the heat gained by the ice is:
Heat gained by ice = 100g * 2.09 J/g°C * (final temperature - 0)

2. Calculate the heat lost by the water:
Heat lost = mass of water * specific heat of water * change in temperature
The mass of water is 100g, the specific heat of water is 4.18 J/g°C, and the change in temperature is the initial temperature of the water minus the final temperature.
So, the heat lost by the water is:
Heat lost by water = 100g * 4.18 J/g°C * (20 - final temperature)

3. Calculate the heat transfer between the iron vessel and the surroundings:
The heat gained by the ice and the heat lost by the water are transferred to the iron vessel, which affects its temperature.
Heat transferred to the iron vessel = mass of iron vessel * specific heat of iron * change in temperature
The mass of the iron vessel is 100g, the specific heat of iron is 0.1 J/g°C, and the change in temperature is the final temperature minus the initial temperature of the iron vessel (which we assume to be the same as the water temperature).
So, the heat transferred to the iron vessel is:
Heat transferred to iron vessel = 100g * 0.1 J/g°C * (20 - final temperature)

4. Apply the principle of heat transfer:
According to the principle of heat transfer, the heat gained by the ice is equal to the heat lost by the water, which is equal to the heat transferred to the iron vessel:
Heat gained by ice = Heat lost by water = Heat transferred to iron vessel
100g * 2.09 J/g°C * (final temperature - 0) = 100g * 4.18 J/g°C * (20 - final temperature) = 100g * 0.1 J/g°C * (20 - final temperature)

Now, you can solve this equation to find the final temperature of the mixture. Simplify and solve for the final temperature.