# Heat

#### kastamonu

In a thermally insulated environment, there is water with a mass of 200 gr at 20 degrees Centigrate.We drop 60 grams of ice into the water with a temperature of -40 degrees. If thermal equilibrium is maintained find the mass of ice and water in the environment?

60.0.5.10+m80=200.1.20
m of ice=35 and mass of water is 225.
According to tthe book answer is 25 and 235.

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#### oz93666

how can there be 225 or 235 gm of water at the end , when to start you have 20gm of water and 60 gm of ice????

#### Woody

It looks to me like a miss-typing
it must be 200g of Water at 20C + 60g of ice at -40C

60.0.5.10+m80=200.1.20
are you using the "." as a multiplication symbol?
are you using the "." as a decimal place?
are you using it as both?
or something different?

As a programmer, I find the use of "*" quite natural for a multiplication symbol,
but this is personal preference.
It matters little as long as it is clear what convention is being employed.

The inclusion of brackets can (hugely) improve the readability of equations.

#### kastamonu

. is for multiplication and , for decimal place. Mass of water is 200 gr.

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#### kastamonu

how can there be 225 or 235 gm of water at the end , when to start you have 20gm of water and 60 gm of ice????
Where is my mistake? Is my answer right or wrong?

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#### HallsofIvy

The point is that mass is conserved. If you started with 200g of water and 60 gm of ice, so you have 260 g all together, then, no matter how much ice melts or water freezes you end with a total of 260 g, not "225 g" or "235 g".

#### kastamonu

But there will be ice and water in the end. The problem asks the amount of ice and water seperately. In the end sum will be 260. But how much of this 260 will be ice and how much will be water?

#### pmahajan18

Hi, firstly we need to know how much latent heat of melting of ice to water is required. It is also to know how much heat is available due to differences of temperature of ice and water. It's seem from the equation not all ice is melted even after equilibrium temperature is achieved and therefore having both ice and water at equilibrium temperature.
Heat balance equation is required to know the equilibrium temperature. Well understood that heat will flow from water to ice. So the temperature of water is decreases while of ice increases. But since total ice is not melted. So it is also possible to use 0 degree temperature as equilibrium temperature. It's my thought