# Calorimetry and Phase change question

• JoshMG
In summary, an insulated beaker with negligible mass contains liquid water with a mass of 0.225 kg and a temperature of 75.8 C. To reach the final temperature of 31.0 C, an ice sheet must be dropped into the water so that the total mass of ice is 0.0890 kg.
JoshMG
The question is:

An insulated beaker with negligible mass contains liquid water with a mass of 0.225 kg and a temperature of 75.8 C.

How much ice at a temperature of -23.6 C must be dropped into the water so that the final temperature of the system will be 31.0 C?
Take the specific heat of liquid water to be 4190 J/kg*K, the specific heat of ice to be 2100 J/kg*k, and the heat of fusion for water to be 334 KJ/kg.

mice=?

This is what I have so far:

mw= 0.225 kg
Tw= 75.8 C
Ti= -23.6 C
mi= ?
Tf= 31.0 C

Cw= 4190 J/kg(K)
Ci= 2100 J/kg(K)
Lf= 334 KJ/kg = 334000J/kg (I would have to convert this right?)

With the information given I come up with these:

Qice warms= mi ci (0- (-5))

Qice melts= mi Lf

Qmix of waters= mi cw (31-0)

Qwater cools= mw cw (31 - 75.8)

Qwater cools = Qice warms + Qice melts + Q mix of waters

so now we can solve the mass of ice. right? But when I calculate it the answer I is really weird.

Last edited:
First if you calculate how much energy is lost due to the water cooling then you can find the mass of ice that would require that amount of energy to heat it to the equilibrium temperature.

okay, but isn't that what I did?

Qwater cools= mw cw (31 - 75.8) (energy lost from ice)

and then i come up with
0 = Qice warms + Qice melts + Q mix of + Qwater cools

Yes that is what you did so how are you calculating the mass of ice? You will notice that you have three terms all containing the mass of the ice so you can easily take it out and rearrange to find the value.

haha okay. I'm doing

mi((2100*5)+(334000)+(4190*31) = 0.225*4190*44.8

mi = 0.0890 kg ... which is wrong.

Why is there a 5 in there? The ice starts at -23.6.

ooo my goodness! thank you so much. i hate when i do that! thank you!

## 1. What is calorimetry?

Calorimetry is the measurement of heat transfer between two substances. It involves using a calorimeter, which is a device that can accurately measure the amount of heat released or absorbed during a chemical reaction or physical change.

## 2. How does a calorimeter work?

A calorimeter works by measuring the temperature change of a substance or system. It consists of an insulated container filled with a known amount of water or other liquid, and a thermometer to measure the temperature change. When a chemical reaction or phase change occurs, the heat released or absorbed is transferred to the water, causing a change in its temperature. By measuring this temperature change, the amount of heat can be calculated.

## 3. What is a phase change?

A phase change is a physical change in which a substance transitions from one state of matter to another. The three main phases of matter are solid, liquid, and gas. During a phase change, the temperature of a substance remains constant, but the heat energy is either absorbed or released.

## 4. How does calorimetry relate to phase changes?

Calorimetry is often used to measure the heat involved in phase changes. When a substance undergoes a phase change, such as melting or boiling, a significant amount of heat is either absorbed or released. By using a calorimeter, the amount of heat can be accurately measured and used to determine the enthalpy of the phase change.

## 5. What are some real-life applications of calorimetry and phase changes?

Calorimetry and phase changes are used in various industries such as food and beverage production, pharmaceuticals, and energy production. For example, in the food industry, calorimetry is used to determine the caloric content of food products. In the pharmaceutical industry, it is used to study the thermal stability of drugs. In energy production, phase changes are used to generate electricity in power plants.

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