Simple Thermal Calculation
If the methods for thermal calculation given below are understood, problems in many practical fields.
What is the energy E J required to increase the temperature of an object M g from T0 °C to T1 °C?
Data to be investigated → Heat capacity of an object Cp J/g/k
* Click here for the Cp values of main substances. As it opens on a separate page, close by clicking on the x mark at the top right of the Webpage. If you do not find the information on the page, search in the chronological scientific tables.
The following equation is obtained as the unit of Cp is J/g/k.
Cp = E/ (T1 - T0)/M J/k/g Equation (1)
To calculate E, the above equation is expressed in terms of E=____________________
E = Cp X M X (T1 - T0) J Required energy based on formula (1), an equation can be obtained for calculating M as well as T1.
M = E/Cp/ (T1 – T0) g Mass of the material heated
T1 = E/M/ Cp + T0 °C End-point temperature
The unit of Cp is expressed as J/k/g, but if there is no g in the data of the chronological scientific tables, then it is also expressed as J/k/mol using mol → (mole). In this case, converting mol to g to obtain J/k/g is necessary.
The weight of 1 mole is said to be the molecular weight.
Molecular weight can also be obtained from data books such as the chronological scientific tables. The molecular weight can be obtained with a simple calculation if the molecular formula is known.
→ Add the atomic weight of the atoms that form the molecule.
For example, the molecular formula of Alumina is Al2O3. Since it consists of 2 Aluminium atoms and 3 Oxygen atoms, from the atomic weight of aluminium 27 and the atomic weight of oxygen 16, the molecular weight of Alumina will be 27 + 27 + 16 + 16 + 16= 102.
In other words, 1 mole of Alumina molecule is approximately 102 grams.
According to the chronological scientific tables, since the heat capacity of Alumina (= Aluminium Oxide Al2O3) at 400K (127°C) is 96 J/k/mol, just divide this by the molecular weight to convert it to the unit of [J/k/g].
Heat capacity Cp of Alumina = 96 / 102 = 0.94 J/k/mol
* The mole is defined as the amount of a chemical substance that contains exactly → 6.02 x 1023 constituent particles (Avogadro's constant). In other words, it is a number with 6 followed by 23 zeros, a number almost approaching infinity (approximately 1 trillion times 1 trillion). The amount cannot be expressed in grams as the molecules are extremely small, and atoms to this extent are required to be collected for expressing in grams. 1 mole of hydrogen atoms is approximately 1 gram and 1 mole of iron atoms is approximately 56 grams.
* 1 mole of any kind of gas at 0°C and atmospheric pressure is 22.4 litres without exception. The volume of gas is inversely proportional to its force and proportional to absolute temperature. For example, 1 mole of oxygen molecule is 22.4 litres at 0°C (273K in terms of absolute temperature). At 1000°C (1273K), this will be 22.4 × (1273/273) = 104.5 litres. K (absolute temperature) can be obtained by adding 273 to the temperature expressed in °C (Celsius))
* If you understand the above, it is easy to find out how many litres X grams of gas is, or how many grams X litres of gas is even if only the molecular weight of the gas is known.
* These thermal calculation equations are valid when thermal efficiency is 100%. However, in practice, thermal efficiency is not 100% in most cases. Heat loss also occurs in most cases due to which amount of electric power required according to the amount of loss has to be taken into consideration and if further possible, a margin should be considered, and a larger value should be adopted. In general, it is about 30% compared to the minimum requirement (on a case by case basis), bring down the electric power using a large electric power with a voltage controller and automatic temperature regulator to create the best conditions.
When the factor of time is added to the problem mentioned above. For example ---
What is the power P W required to increase the temperature of an object M g from T0 °C to T1 °C in time t s?
For adding the factor of time, energy is expressed in Watts rather than Joules.
1 Watt is 1 Joule per second.
1 W= 1 J/s
From E = P X t J
Cp = P X t / (T1-T0)/M J/k/g Equation (2)
This time, calculate P is required to be calculated, if you modify the above equation into P = Cp X M X (T1- T0) / t W
based on equation (2), equations can be obtained for calculating M, T1 as well as t.
M = P x t / Cp / (T1- T0) g Mass of the material to be heated
T1 = P X t / M / Cp + T0 °C End- point temperature
t = Cp X (T1- T0) X M / P s Time required