Physics · Thermal Properties Of Matter · NEET
It is the heat you must give to 1 mole of a substance to make its temperature rise by 1 kelvin. A mole is a fixed count of particles (6.022 x 10^23). So instead of measuring per gram or per kilogram, you measure per mole. The formula is C = Q / (n x delta T), where Q is heat in joules, n is moles, and delta T is the temperature rise. If 1 mole needs more heat for the same 1 K rise, its molar heat capacity is larger.
Both tell how much heat raises temperature by 1 K, but the amount of substance is measured differently. Specific heat capacity (s) is PER UNIT MASS (per kg), unit J/kg/K. Molar heat capacity (C) is PER MOLE, unit J/mol/K. They are linked by C = s x M, where M is the molar mass in kg/mol. Example: for water s = 4186 J/kg/K and M = 0.018 kg/mol, so C = 4186 x 0.018 = about 75.3 J/mol/K.
The SI unit is joule per mole per kelvin, written J/mol/K or J mol^-1 K^-1. This comes straight from C = Q / (n x delta T): Q is in joules, n is in moles, and delta T is in kelvin. Since a change of 1 kelvin equals a change of 1 degree Celsius, the unit can also be written J/mol/degree Celsius. Note NCERT calls it 'molar specific heat capacity' - it means the same thing.
Multiply the specific heat by the molar mass: C = s x M. Keep units consistent - use s in J/kg/K and M in kg/mol so the answer comes out in J/mol/K. For example, aluminium has s = 900 J/kg/K and M = 0.027 kg/mol, so C = 900 x 0.027 = 24.3 J/mol/K. This is why many solids have molar heat capacity near 25 J/mol/K (the Dulong-Petit rule).
For a gas, the heat needed for 1 K rise depends on whether the gas is allowed to expand. At constant volume (Cv) no work is done, so all heat raises the internal energy. At constant pressure (Cp) the gas also expands and does work, so it needs extra heat. That is why Cp is larger than Cv, and for an ideal gas they satisfy Cp - Cv = R. For solids and liquids this difference is tiny, so we usually quote just one C.
Two bodies have different thermal (heat) capacities. One of them is at 100 degrees Celsius and the other at 0 degrees Celsius. If the two are brought into contact in an isolated system (no heat loss to surroundings), the final common temperature will be:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Yes. NCERT writes it as 'molar specific heat capacity' and gives the symbol C with unit J/mol/K. Most textbooks and NEET questions shorten it to 'molar heat capacity'. They mean the heat needed per mole for a 1 K rise.
C = Q / (n x delta T), where Q is heat supplied (joules), n is number of moles, and delta T is the temperature change (kelvin). Rearranged, the heat is Q = n x C x delta T.
No. Because it is defined per mole, it is a property of the substance itself, not of how much you have. It does depend on the nature of the substance, its temperature, and (for gases) the conditions like constant volume or constant pressure.
About 25 J/mol/K, close to 3R (where R = 8.314 J/mol/K). This is the Dulong-Petit rule and it holds well for many solids at room temperature.
C = s x M, where s is the specific heat capacity (J/kg/K) and M is the molar mass (kg/mol). Multiplying by molar mass converts 'per kilogram' into 'per mole'.
