How Do You Calculate the Final Mass of Water in a Calorimetry Experiment?

In summary: CucΔTCu + mH20cΔTH20 + micecΔTice + miceL) / (cΔTsteam + Lsteam)To check, the units of the left hand side is kg, that of the right hand side is kgJ/(J/K + J/kg) = kg, so it is correct.This is the solution to the problem:In summary, a 0.080kg copper container with a specific heat of 387Jkg-1K-1 contains 0.30kg of water and 0.040kg of ice at 0°C. When steam at 100°C is passed into the container, the temperature stabilizes
  • #1
unknown217
2
0

Homework Statement


A 0.080kg copper container (specific heat: 387Jkg-1K-1) contains 0.30kg of water and 0.040kg of ice at 0°C. Steam at 100°C is passed into the water and its temperature stabilizes at 20.0°C. Find the mass of the water left in the container assuming the system is insulated.

Homework Equations


Q= mcΔT
Q= mL

The Attempt at a Solution


Q lost = Q gained
msteamcΔT + msteamL = mCucΔT + mH20cΔT + micecΔT + miceL
msteam = mCucΔT + mH20cΔT + micecΔT + miceL / cΔTsteam + Lsteam
Total mass water= mass steam + water + ice

Is this correct?
Is ΔT for steam -80 (20-100°C)?
 
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  • #2
unknown217 said:

Homework Statement


A 0.080kg copper container (specific heat: 387Jkg-1K-1) contains 0.30kg of water and 0.040kg of ice at 0°C. Steam at 100°C is passed into the water and its temperature stabilizes at 20.0°C. Find the mass of the water left in the container assuming the system is insulated.

Homework Equations


Q= mcΔT
Q= mL

The Attempt at a Solution


Q lost = Q gained
msteamcΔT + msteamL = mCucΔT + mH20cΔT + micecΔT + miceL
msteam = mCucΔT + mH20cΔT + micecΔT + miceL / cΔTsteam + Lsteam
Total mass water= mass steam + water + ice

Is this correct?
Is ΔT for steam -80 (20-100°C)?

Welcome to PF!

Do not use the same symbol ΔT for different things. The change of temperature of water is not the same as the change of temperature of the deposited steam.
Your equation means that the heat supplied by the steam is equal to the heat absorbed by the colder parts of the system.
It is right that the change of temperature is -80° for the deposited steam, but you have to use 80° when you calculate the supplied heat.
The equation for msteam is not correct without parentheses around cΔTsteam + Lsteam

ehild
 
  • #3
msteam = mCucΔTCu + mH20cΔTH20 + micecΔTice + miceL / (cΔTsteam + Lsteam)

Is this right?
 
  • #4
You need parentheses also around the nominator. And be sure using correct sign in the denominator.

ehild
 
  • #5


Yes, your attempt at a solution is correct. The ΔT for the steam would be -80°C since it is initially at 100°C and then cools to 20°C when it reaches thermal equilibrium with the water.
 

1. What is the purpose of calorimetry in determining specific heat?

Calorimetry is a technique used to measure the amount of heat released or absorbed during a chemical or physical process. By using this method, we can determine the specific heat capacity of a substance, which is the amount of heat needed to raise the temperature of one gram of the substance by one degree Celsius.

2. How is calorimetry used to determine specific heat?

To determine specific heat using calorimetry, we measure the temperature change of a known mass of a substance as it absorbs or releases heat. By knowing the amount of heat transferred, the mass of the substance, and the change in temperature, we can calculate the specific heat of the substance using the equation Q = m x c x ΔT, where Q is the heat transferred, m is the mass, c is the specific heat, and ΔT is the change in temperature.

3. What are the units for specific heat?

The units for specific heat depend on the units used for heat, mass, and temperature. In the SI system, the units for specific heat are joules per gram per degree Celsius (J/g·°C). In the imperial system, the units are British thermal units per pound per degree Fahrenheit (BTU/lb·°F).

4. How does the specific heat of a substance affect its temperature change?

The specific heat of a substance is a measure of how much heat is needed to change its temperature. A substance with a high specific heat will require more heat to raise its temperature compared to a substance with a low specific heat. This means that substances with higher specific heat will have a smaller temperature change for the same amount of heat applied.

5. What are some applications of specific heat and calorimetry?

Specific heat and calorimetry have various practical applications in fields such as chemistry, physics, and engineering. They are used to determine the energy content of foods, measure energy efficiency in buildings, and study the thermal properties of materials. They are also essential in understanding and controlling heat transfer processes in industrial processes and power generation.

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