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# Is $H = mCT$ and $q = mCT$ the same thing? If so, which is more scientific?

Last updated date: 23rd Apr 2024
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Hint: When a process occurs, the heat evolved is equal to the change in enthalpy. Enthalpy is equal to the sum of internal energy and product of pressure and volume. The equation can be given as: $H = U + PV$
At constant pressure, the heat evolved is equal to the change in enthalpy. Enthalpy is a state function which depends on other state functions like Temperature (T), Pressure (P) and Internal energy (U). The change in enthalpy is given as the enthalpy change between initial and final states: $\Delta H = \Delta U + P\Delta V$

Enthalpy in molar terms can be given as Molar Enthalpy when enthalpy is divided by the no. of moles ( $\Delta {H_m}$ ). Enthalpy is a state function as it doesn’t depend on the path that is followed by the system. If a non-expansion work takes place and the pressure is held constant, then the change in enthalpy is equal to the heat consumes by the system i.e. $\Delta H = q$ -- (1)
This is used to determine the reaction is endothermic or exothermic. At constant pressure, when heat is absorbed, it is endothermic and when heat is evolved it is exothermic. According to the equation, if the internal energy increases then the enthalpy increases as the temperature increases. Using this we can derive the relationship: $C = \dfrac{q}{{\Delta T}}$
As constant pressure, the equation can be written as: ${C_p} = {\left( {\dfrac{{\Delta H}}{{\Delta T}}} \right)_p}$
Therefore, we can say that $\Delta H = {C_p}\Delta T$ . The molar enthalpy can be given as:
$\Delta H = m{C_p}\Delta T$ -- (2)
From equation (1) and (2) we get that $q = m{C_p}\Delta T$
Therefore, both the equations $H = mCT$ and $q = mCT$ are the same.

Note:
When heat is added, the temperature will change by a certain amount. The relationship between heat and temperature differs in every substance by the amount of specific heat. The relationship is hence given as: $q = mC\Delta T$
Where, q = heat (joules, J), m= mass of the substance (kg), c= specific heat (J/kg.K), $\Delta T$ = change in temperature.