Need Help Calculating Energy Required to Raise Magnesium Temp

In summary, the given conversation discusses the temperature-dependent molar specific heat capacity and its calculation for magnesium. The energy required to raise the temperature of 15g of magnesium from 30 C to 300 C can be calculated using the formula provided. The conversation also mentions the use of an electric underfloor heater in a 15mm thick concrete slab and the time required to change the temperature from 23.5 C to 21 C with varying outside temperature and heat transfer output. The equation provided can be used to find the average value of specific heat and calculate the time needed for temperature changes."
  • #1
davidray
7
0
Any help on this quistion would be greatly appreciated. I have no idea ho to answere it, and can't find anything in my nothes or books anywhere.

The temperature-dependent molar specific heat capacity at constant pressure of many substances is given by: c =a+2bT−cT^−2

For magnesium, the numerical values of the constants are: a=25.7, b=3.13x10^-3, c=3.27x10^5

where c has units J/Kxmol

Calculate the energy required to raise the temperature of 15g of Megnesium from 30 C to 300 C.

I have tried using the formula to qenerate a specific heat capacity for each temperature, but just seem to get crazy numbers that don't make any sense!

Thanks for the help!
 
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  • #2


You can find the average value of the specific heat over the temperature range from:

C_avg = [itex]\frac{1}{Tf-To}[/itex][itex]\int[/itex][itex]\frac{To}{Tf}[/itex]C(T) dt

Then compute the energy from:

E = m C_avg (Tf - Ti)
 
  • #3


any help for the following qestion will be appriciated

15mm thick concrete slab have an electric underfloor heater running in off peak time and release storage heat during day time then how much time its to reduce temp. from 23.5 at6:00am to 21 degree and with the variable outside temp. during day.outside temp is 8 degree and reuire temp. 19 at 6:00am and heat transfer output is 41.62w/m2

and how much time its to increse the temp during running off peak time
 
  • #4


apatel said:
any help for the following qestion will be appriciated

15mm thick concrete slab have an electric underfloor heater running in off peak time and release storage heat during day time then how much time its to reduce temp. from 23.5 at6:00am to 21 degree and with the variable outside temp. during day.outside temp is 8 degree and reuire temp. 19 at 6:00am and heat transfer output is 41.62w/m2

and how much time its to increse the temp during running off peak time
reply with the equation
 
  • #5


Hi there,

Calculating the energy required to raise the temperature of a substance can be a bit tricky, but I'll try to break it down for you. First, let's start by converting the mass of magnesium from grams to moles. We can do this by using the molar mass of magnesium, which is 24.31 g/mol.

15g of magnesium / 24.31 g/mol = 0.617 moles of magnesium

Now, we can use the specific heat capacity formula you mentioned to calculate the specific heat capacity for each temperature. Remember to convert the temperature from Celsius to Kelvin by adding 273.15.

For 30°C:
c = 25.7 + 2(3.13x10^-3)(303.15) - 3.27x10^5(303.15)^-2
c = 25.7 + 1.898 + 3.27x10^5(9.36x10^-6)
c = 25.7 + 1.898 + 3.06
c = 30.658 J/Kxmol

For 300°C:
c = 25.7 + 2(3.13x10^-3)(573.15) - 3.27x10^5(573.15)^-2
c = 25.7 + 3.584 + 3.27x10^5(3.66x10^-6)
c = 25.7 + 3.584 + 1.198
c = 30.482 J/Kxmol

Now we can use the specific heat capacity to calculate the energy required to raise the temperature. We can use the equation q = mcΔT, where q is the energy in joules, m is the mass in kilograms, c is the specific heat capacity in J/Kxkg, and ΔT is the change in temperature in Kelvin.

For 30°C:
q = (0.617 mol)(0.02431 kg/mol)(30.658 J/Kxmol)(300.15 K - 273.15 K)
q = 2.6 J

For 300°C:
q = (0.617 mol)(0.02431 kg/mol)(30.482 J/Kxmol)(573.15 K - 303.15 K)
q = 201.5 J

So, the energy
 

1. What is the formula for calculating the energy required to raise magnesium temperature?

The formula for calculating the energy required to raise magnesium temperature is E = m x c x ΔT, where E is the energy in Joules, m is the mass of magnesium in grams, c is the specific heat capacity of magnesium in J/g℃, and ΔT is the change in temperature in ℃.

2. How do I determine the specific heat capacity of magnesium?

The specific heat capacity of magnesium can be found in reference tables or calculated using the specific heat capacity of magnesium oxide (MgO) and the Law of Dulong and Petit. According to this law, the specific heat capacity of an element is approximately 3R, where R is the gas constant (8.314 J/mol·K). Therefore, the specific heat capacity of magnesium is 3 x 8.314 = 24.942 J/mol·K.

3. Can I use the same formula to calculate the energy required to raise the temperature of other substances?

Yes, the same formula can be used to calculate the energy required to raise the temperature of other substances, as long as the specific heat capacity and mass of the substance are known.

4. How does the temperature of the surroundings affect the calculation of energy required to raise magnesium temperature?

The temperature of the surroundings does not directly affect the calculation of energy required to raise magnesium temperature. However, it can indirectly affect the result if there is heat transfer between the surroundings and the magnesium. In this case, the energy required to raise the temperature will be higher to account for the heat lost to the surroundings.

5. Is there a simpler way to calculate the energy required to raise magnesium temperature?

The formula E = m x c x ΔT is the simplest way to calculate the energy required to raise magnesium temperature. However, if the mass and specific heat capacity of magnesium are not known, the energy can also be calculated by measuring the heat released by the burning of magnesium and using the equation Q = mcΔT, where Q is the heat in Joules, m is the mass of water in grams, c is the specific heat capacity of water (4.184 J/g℃), and ΔT is the change in temperature of the water.

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