I am trying to calculate heat transfer between two objects. The units are as follows:
m1: 100 g
t1: 10 degrees C
spec heat 1: 1.00 cal/g degree C
m2: 200 g
t2: 90 degrees C
spec heat 2: 0.2 cal/gm degree C
I set Q1 = Q2
m1 x spec heat 1 x delta T1 = m2 x spec heat 2 x delta T2 and solved for T final where Tfinal 1 = Tfinal 2.
My numbers aren't working out.
aaaaaaaaahhhh. got it. you have to add them and set them equal to zero.
Yes, you add them. One term is positive and the other is negative. The sum is zero.
To calculate the heat transfer between two objects, you can use the formula:
Q1 = Q2
Where,
Q1 = m1 x spec heat 1 x delta T1 (heat transferred by object 1)
Q2 = m2 x spec heat 2 x delta T2 (heat transferred by object 2)
m1 = mass of object 1
m2 = mass of object 2
spec heat 1 = specific heat capacity of object 1
spec heat 2 = specific heat capacity of object 2
delta T1 = change in temperature for object 1
delta T2 = change in temperature for object 2
Assuming that the objects are in thermal equilibrium at the final temperature (Tfinal), you can set Tfinal1 = Tfinal2 and solve for the final temperature.
Let's plug in the given values and calculate:
Given:
m1 = 100 g
t1 = 10 degrees C
spec heat 1 = 1.00 cal/g degree C
m2 = 200 g
t2 = 90 degrees C
spec heat 2 = 0.2 cal/gm degree C
Using the formula Q1 = Q2:
m1 x spec heat 1 x delta T1 = m2 x spec heat 2 x delta T2
Now, let's calculate the difference in temperatures (delta T).
delta T1 = Tfinal - t1
delta T2 = Tfinal - t2
Substituting the values, the equation becomes:
100 g x 1.00 cal/g degree C x (Tfinal - 10 deg C) = 200 g x 0.2 cal/gm degree C x (Tfinal - 90 deg C)
Simplifying the equation:
100 cal/degree C x (Tfinal - 10 deg C) = 40 cal/degree C x (Tfinal - 90 deg C)
Now, we can solve for Tfinal:
100Tfinal - 1000 = 40Tfinal - 3600
60Tfinal = 2600
Tfinal = 2600 / 60
Tfinal ≈ 43.33 degrees C
Therefore, the final temperature of both objects should be approximately 43.33 degrees Celsius.
To calculate the heat transfer between two objects, you can use the equation:
Q = m * c * ΔT
Where:
Q is the heat transfer (in calories or joules),
m is the mass of the object (in grams or kilograms),
c is the specific heat capacity of the object (in cal/g°C or J/kg°C), and
ΔT is the change in temperature (in °C or Kelvin).
In your case, you have two objects with different masses and specific heat capacities. Let's calculate the heat transfer between them.
Object 1:
- Mass (m1) = 100 g
- Initial temperature (t1) = 10 °C
- Specific heat capacity (spec heat 1) = 1.00 cal/g°C
Object 2:
- Mass (m2) = 200 g
- Initial temperature (t2) = 90 °C
- Specific heat capacity (spec heat 2) = 0.2 cal/g°C
You mentioned you set Q1 = Q2, which means the heat transfer is the same for both objects. However, it seems like you are trying to solve for the final temperature (T final), assuming both objects reach the same temperature in the end.
The correct equation to use would be:
m1 * spec heat 1 * ΔT1 = m2 * spec heat 2 * ΔT2
Let's solve for ΔT1 and ΔT2:
ΔT1 = (m2 * spec heat 2 * ΔT2) / (m1 * spec heat 1)
ΔT2 = (m1 * spec heat 1 * ΔT1) / (m2 * spec heat 2)
After finding the values of ΔT1 and ΔT2, you can calculate the final temperatures:
T final 1 = t1 + ΔT1
T final 2 = t2 - ΔT2
Please make sure to substitute the units consistently (e.g., grams for mass, degrees Celsius for temperature, and cal/g°C for specific heat capacity) in the calculations. Double-check your calculations to ensure accurate results.