Chemistry · Thermodynamics · NEET
Molar heat capacity is the heat you must give to ONE mole of a substance to make its temperature go up by ONE degree (1 kelvin or 1 °C). NCERT writes it as Cm. Think of it as the 'price in heat' to warm up one mole by one step. It tells you how much energy that one mole can soak up before it gets hotter.
There are two ways to write it. First, from the heat directly: Cm = q / (n × ΔT), where q is heat given, n is the number of moles, and ΔT is the temperature rise. Second, from heat capacity: Cm = C / n, where C is the total heat capacity of the sample. Both give the same answer because Cm is always 'per one mole'.
The unit of Cm is joule per kelvin per mole, written J K⁻¹ mol⁻¹ (you may also see J mol⁻¹ K⁻¹ — it is the same thing). This is because Cm = heat (J) divided by moles (mol) and by temperature change (K). For NEET, always match units: if heat is in joules, the answer is in J K⁻¹ mol⁻¹.
Heat capacity C is for the WHOLE sample you have — it depends on how much substance is there, so it is an extensive property. Molar heat capacity Cm is for exactly ONE mole — it does NOT depend on the amount, so it is intensive. Simple link: Cm = C / n. If you have 2 moles and C = 50 J/K, then Cm = 25 J K⁻¹ mol⁻¹.
Molar heat capacity is an INTENSIVE property. NCERT lists molar volume (Vm) and molar heat capacity (Cm) as examples of molar (intensive) quantities. The word 'molar' fixes the amount at one mole, so the value no longer changes with sample size. That is why Cm of water is the same whether you have 1 mole or 100 moles.
Both are intensive, but they use a different 'amount' base. Molar heat capacity is per ONE MOLE (unit J K⁻¹ mol⁻¹). Specific heat capacity is per ONE UNIT MASS, like per gram or per kg (unit J K⁻¹ g⁻¹). You convert between them using molar mass M: Cm = specific heat × molar mass. Do not mix the two in a formula.
NEET calorimetry and first-law numericals often give you Cm (or Cp and Cv) and ask for heat q = n × Cm × ΔT. If you confuse Cm with specific heat or with total heat capacity C, you divide or multiply by the wrong 'amount' and the answer is wrong. Knowing the exact definition and unit keeps your numerical steps clean.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is the heat required to raise the temperature of one mole of a substance by one degree (1 K). Formula: Cm = q / (n × ΔT) = C / n.
J K⁻¹ mol⁻¹ (joule per kelvin per mole). It may also be written J mol⁻¹ K⁻¹, which means the same.
Intensive. It is fixed at one mole, so it does not depend on the amount of substance, just like temperature or density.
Use q = n × Cm × ΔT, where n is moles, Cm is molar heat capacity, and ΔT is the temperature change.
Cm = specific heat capacity × molar mass. Molar heat capacity is per mole; specific heat is per unit mass.
