# A $75.0\;\text{g}$ sample of a metal is heated by adding $450\;\text{J}$ of heat. If it's temperature increases from $22 ^{\circ} \text{C}$to $37 ^{\circ} \text{C}$, what is the molar mass of the metal?

$\begin{array}{1 1} 69\;g/mol \\ 65\;g/mol \\ 72\;g/mol \\ 62\;g/mol \end{array}$

An object's heat capacity (symbol C) is defined as the ratio of the amount of heat energy transferred to an object and the resulting increase in temperature of the object. More generally, because heat capacity does depend upon temperature, specific heat capacity, often called simply specific heat, which is the heat capacity per unit mass of a material, should be written as $C(T) = \large\frac{\Delta Q}{m \Delta T}$
Given $\Delta Q = 450 \text {J}$ and $\Delta T = 37 - 23 = 15 ^{\circ}$ and mass $m = 75g$, Specific Heat Capacity $= \large\frac{450 J}{75.0g \times 15 ^{\circ}}$$= 0.4\; J/g\;^{\circ}C Dulongâ€“Petit law in modern terms is that, regardless of the nature of the substance or crystal, the specific heat capacity c of a solid substance (measured in joule per kelvin per kilogram) is equal to 3R/M, where R is the gas constant (measured in joule per kelvin per mole) and M is the molar mass (measured in kilogram per mole). Universal gas constant, R = 8.3144621(75) \;J/molK Using Dulong-Petit's law, M = molar mass of the metal = \large\frac{3R}{C}$$ = \large\frac{3 \times 8.314 J/molK} {0.4 J/g ^{\circ}C}$$= 62 g/mol$