# Need help with basic specific heat capacity problem

• lilmul123
In summary, the specific heat capacity of a certain metal can be determined by measuring the temperature change when a piece of the metal is heated and placed in an insulated container with water. Using the equations Q = mc(deltaT) and Q1 + Q2 + Q3 = 0 and the known capacity of water, the specific heat capacity of the metal was found to be approximately 0.45 kJ/kg*K.
lilmul123

## Homework Statement

The specific heat of a certain metal can be determined by measuring the temperature change that occurs when a piece of the metal is heated and then placed in an insulated container that is made of the same material and contains water. Suppose the piece of metal has a mass of 86 g and is initially at 100°C. The container has a mass of 162 g and contains 504 g of water at an initial temperature of 20.0°C. The final temperature is 21.4°C. What is the specific heat of the metal?

## Homework Equations

Q = mc(deltaT)
Q1 + Q2 + Q3 = 0

4.18 kJ/kg*K is the known capacity of water.

## The Attempt at a Solution

I set c equal to the specific heat capacity I'm looking for. Q1 is the metal going into the bucket, Q2 is the metal of the bucket, and Q3 is the water itself. Since Q1 and Q2 are the same metal, their c's are the same.

My equation looks like this where the specific heat capacities are in kJ/kg*K:

(.086)(c)(-78.6) + (.162)(c)(1.4) + (.504)(4.18)(1.4) = 0

Solving for c gives me 2.214 kJ/kg*K which is incorrect. Have I missed a step?

Check your algebra. I get 0.45 kJ/kg*K using your equation.

lilmul123 said:
(.086)(c)(-78.6) + (.162)(c)(1.4) + (.504)(4.18)(1.4) = 0

Solving for c gives me 2.214 kJ/kg*K which is incorrect. Have I missed a step?

Check your algebra again when you solve for c. It looks like you may have made a mistake. I'm getting about 0.45.

Oh geez, I divided by the wrong side in my last step of the algebra. Thanks!

## 1. What is specific heat capacity?

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius.

## 2. How do I calculate specific heat capacity?

The formula for specific heat capacity is Q = mCΔT, where Q is the amount of heat transferred, m is the mass of the substance, C is the specific heat capacity, and ΔT is the change in temperature.

## 3. What units are used to measure specific heat capacity?

Specific heat capacity is typically measured in joules per gram per degree Celsius (J/g°C) or calories per gram per degree Celsius (cal/g°C).

## 4. What factors affect specific heat capacity?

The specific heat capacity of a substance is affected by its composition, density, and temperature. It also varies depending on the phase of the substance (solid, liquid, or gas).

## 5. Why is specific heat capacity important?

Specific heat capacity is important because it helps us understand how substances respond to changes in temperature and how much energy is required to heat or cool them. It also plays a crucial role in many scientific fields, such as thermodynamics and engineering.

Replies
9
Views
2K
Replies
6
Views
2K
Replies
6
Views
2K
Replies
3
Views
3K
Replies
3
Views
1K
Replies
16
Views
4K
Replies
5
Views
905
Replies
3
Views
4K
Replies
3
Views
1K
Replies
8
Views
6K