Q=mcT heat problem, were did i go wrong?

  • Thread starter Senjai
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In summary, the conversation was about solving a heat problem involving a sample of aluminum and given heat energy. The correct equation to use is Q=mcΔT, and to find the final temperature, T', the formula is T' = Q/mc + T. The final answer should be 170 degrees Celsius.
  • #1
Senjai
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[SOLVED] Q=mcT heat problem, were did i go wrong?

Homework Statement


If a 45g sample of aluminum at 22 degrees C is given 6.0 x 10^3 J of heat, what will its final temperature be?


Homework Equations


[tex]Q = mc \Delta T[/tex]


The Attempt at a Solution


i found in my textbook that aluminum has a specific heat capacity of 900
so c = 900.

[tex]Q = mc \Delta T [/tex]
[tex]Q = mc( T' - T ) [/tex]
[tex]T' - T = \frac{Q}{mc} [/tex]
[tex]T' = \frac{Q + T}{mc}[/tex]
[tex]T' = \frac{(6.0 x 10^3 J) + 22\deg}{(0.045kg)(900)} [/tex]
 
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  • #2
i got 148 Deg C which is wrong... i need 170 Deg C
 
  • #3
You've just rearranged wrongly. Its not (Q+T)/mc.
 
  • #4
so is it [tex] T' = \frac{Q}{mc} + T [/tex] ??
 
  • #5
That should work.
 
  • #6


kurdt ,
what would the worked out solution look like for the last step?
 

1. What is the meaning of Q=mcT in a heat problem?

Q=mcT is the equation used to calculate the amount of heat energy transferred in a system. Q represents the amount of heat energy, m is the mass of the object, c is the specific heat capacity of the material, and T is the change in temperature.

2. What does the value of c represent in the Q=mcT equation?

The value of c represents the specific heat capacity of the material, which is the amount of heat energy required to raise the temperature of 1 gram of the material by 1 degree Celsius.

3. How do I know if I have correctly calculated the value of Q in a heat problem?

You can check your calculation by making sure the units for each variable in the Q=mcT equation match up. The units for Q should be in joules (J), the units for m should be in grams (g), the units for c should be in joules per gram per degree Celsius (J/g°C), and the units for T should be in degrees Celsius (°C).

4. What are the common mistakes made when solving a Q=mcT heat problem?

Some common mistakes include using the wrong units for the variables, not converting units to match, and forgetting to include the change in temperature (T) in the equation. It is also important to make sure that the specific heat capacity (c) is for the correct material being used in the problem.

5. How do I know if I have correctly solved a Q=mcT heat problem?

To ensure that you have correctly solved a Q=mcT heat problem, you can check your answer using the equation Q=mcT. Plug in the values you calculated for m, c, and T and make sure the resulting value for Q matches your initial calculation. You can also compare your answer to similar problems or ask a peer or instructor to check your work.

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