Specific Heat Capacity Problem.(Please check.)

In summary, the metal cools down by 30.87C after being dropped into the beaker of water with an initial temperature of 21C.
  • #1
shulien
2
0
This is CALORIMETRY PROBLEM.

A 0.050kg metal bolt is heated to an unknown initial temperature. It is then dropped into a beaker containing 0.15kg of water with an initial temperature of 21.0 C. The bolt and metal then reach a final temperature of 25.0 C. If the metal has a specific heat capacity of 899 J/kg*C, find the initial temperature of the metal.

the solution is:

Change in Temp of metal = (C of water *mass of water* Change in temp of water)/(C of metal*mass of metal)

Change of temp. of metal = [(4186 J/kg*C)(0.15kg)(25C-21C)]/[(899 j/kg*C)(0.050kg)
Change of temp. of metal = 55.87C

Change in temperature = Final Temperature-Initial Temperature
Initial Temperature = Final Temp.-Change in Temp
=25C-55.87C
= -30.87C


i want to ask why is the answer +80.87C from the book, instead of -30.87C?

i hope you could explain so i can also explain it to my students. is the sign of the answer has something to do with the HEAT REMOVAL and HEAT ABSORPTION?

Thanks!
 
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  • #2
shulien said:
the solution is:

Change in Temp of metal = (C of water *mass of water* Change in temp of water)/(C of metal*mass of metal)
This is off by a minus sign. The net change in thermal energy of "metal + water" is zero, so:
Change in Temp of metal = - (C of water *mass of water* Change in temp of water)/(C of metal*mass of metal)

Change of temp. of metal = [(4186 J/kg*C)(0.15kg)(25C-21C)/[(899 j/kg*C)(0.050kg)
Change of temp. of metal = 55.87C
The change in temp of the metal is -55.87C, not +. (The metal cools down.)

Change in temperature = Final Temperature-Initial Temperature
Initial Temperature = Final Temp.-Change in Temp
=25C-55.87C
= -30.87C
25C - (-55.87C) = +80.87C
i hope you could explain so i can also explain it to my students. is the sign of the answer has something to do with the HEAT REMOVAL and HEAT ABSORPTION?
Just keep in mind that the "heat" gained by the water must equal the "heat" removed from the metal. In terms of Q: For the water, Q = + (it heats up); for the metal, Q = - (it cools down). The net Q is zero.
 
  • #3
Doc Al said:
This is off by a minus sign. The net change in thermal energy of "metal + water" is zero, so:
Change in Temp of metal = - (C of water *mass of water* Change in temp of water)/(C of metal*mass of metal)


The change in temp of the metal is -55.87C, not +. (The metal cools down.)


25C - (-55.87C) = +80.87C

Just keep in mind that the "heat" gained by the water must equal the "heat" removed from the metal. In terms of Q: For the water, Q = + (it heats up); for the metal, Q = - (it cools down). The net Q is zero.


thanks for the reply.
:smile:
 

1. What is specific heat capacity and how is it measured?

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. It is measured in units of joules per gram per degree Celsius (J/g°C).

2. How is specific heat capacity used in practical applications?

Specific heat capacity is used in many practical applications, such as determining the amount of heat needed to raise the temperature of a substance in cooking or industrial processes. It is also used in thermodynamics to calculate the efficiency of heat engines and in materials science to understand the thermal properties of different materials.

3. How does specific heat capacity vary between different substances?

Specific heat capacity varies between different substances due to their different molecular structures and compositions. For example, substances with stronger intermolecular forces tend to have higher specific heat capacities because more energy is required to break these forces and raise the temperature of the substance.

4. How does specific heat capacity change with temperature?

In general, specific heat capacity increases with temperature due to the increasing vibrational and rotational energies of molecules as temperature rises. However, some substances may have a specific heat capacity that decreases with temperature due to changes in their molecular structure.

5. How is specific heat capacity related to other thermodynamic properties?

Specific heat capacity is related to other thermodynamic properties, such as enthalpy and entropy, through the heat capacity equation. This equation relates the change in heat (Q) to the change in temperature (ΔT) and the specific heat capacity (C) of a substance: Q = mCΔT, where m is the mass of the substance.

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