Heat Capacity v.s Specific Heat Capacity

Heat capacity, C Specific heat capacity, c
Definition Amount of heat required to increase the temperature of the object by 1 K or 1oC. Amount of heat required to increase the temperature of 1 kg (unit mass) of the substance by 1 K or 1oC.
SI unit J/K or J/oC or JK-1 or JoC-1 J/(kg K) or J/(kgoC) or Jkg-1K-1
or J kg-1oC-1
Formula             C = Q/∆θ
where
∆θ = change in temperature (in K or oC);
Q = thermal energy absorbed in (J)		             c = Q/(m * ∆θ)
where
∆θ = change in temperature (in K or oC);
m = mass (in kg);
Q = thermal energy absorbed in (J)
Factors that affect it Mass, type of substance

Different (bigger) mass of same material has different (bigger) heat capacity;
Same mass of different material has different heat capacity;
Different mass of different material may or may not have same heat capacity.
=> It is more meaningful to compare specific heat capacity for different materials.		 Type of substance only

For same material, the specific heat capacity is the same regardless of the mass.
Relationship C = mc
Note:
  • For same amount of thermal energy supplied, the substance with lower specific heat capacity will be heated up faster than that with higher specific heat capacity. 
  • When doing calculation, first think about which material releases thermal energy (temperature decreases) and which one gains thermal energy (temperature increases), and these two should be the same with the assumption of no energy is lost to the surrounding (which is always the case for calculation). 

Example:

A piece of hot coal of mass 50 g at a temperature of 200oC is dropped into 150 g of water at a temperature of 25oC. Calculate the final temperature reached. (The specific heat capacity of coal and water are 710 Jkg-1K-1 and 4200 Jkg-1K-1 respectively.)

Let final temperature be θ.
Thermal energy lost by coal = thermal energy gained by water
                              mc cc ∆θc = mw cw ∆θw
         0.05 * 710 * (200 – θ) = 0.15 * 4200 * (θ-25)
                                            θ = 38.4oC

Recall that change in temperature in  ⁰C is same as change in temperature in K. Therefore, you do not need to convert the unit for temperature change. This is discussed under Kelvin Scale.
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