Heat and temperature are not the same thing.
It takes more heat to change the temperature of a full saucepan of water than it does to an empty pan by the same amount. Heat flow from hot to cold objects: it is the transfer of energy due to a temperature difference. "Cold" does
not flow from cold objects to hot objects!
The temperature change brought about by supplying an amount of heat depends on:
 the substance being heated up (it takes more heat to warm up the water inside the saucepan than the metal of the saucepan itself
 the amount of the substance (it takes more heat to warm up a full saucepan than a half empty one)
Copper has a
low heat capacity meaning that a small amount of heat produces a large temperature change. Water has a
high heat capacity meaning that a large amount of heat is required to warm it up.
We use two common measures of amount of stuff in science: mass and number of moles. Depending on which we are using, there are therefore two different heat capacity values for each substance:
 If the amount of material is known in grams, we use the specific heat capacity. This has the symbol c and units J g^{1} K^{1}.
 If the amount of material is known in moles, we use the molar heat capacity. This has the symbol C and units J mol^{1} K^{1}.
Substance 
Phase 
c_{} (J g^{1} K^{1}) 
C (J mol^{1} K^{1}) 
Aluminium 
solid 
0.897 
24.2 
Copper 
solid 
0.385 
24.47 
Diamond 
solid 
0.5091 
6.115 
Ethanol 
liquid 
2.44 
112 
Glass 
solid 
0.84 

Gold 
solid 
0.129 
25.42 
Granite 
solid 
0.790 

Graphite 
solid 
0.710 
8.53 
Iron 
solid 
0.450 
25.1 
Lead 
solid 
0.127 
26.4 
Silver 
solid 
0.233 
24.9 
Water at 25 °C 
liquid 
4.1813 
75.327 
The heat,
q is thus related to the temperature change, Δ
T, by:
For a mass m:   For a number of moles n: 
q = m × c × ΔT 

q = n × C × ΔT 
ΔT = q / (m × c) 

ΔT = q / (n × C) 
Points to note:
 ΔT is the temperature difference between the initial temperature, T_{i}, and the final temperature, T_{f} such that:
ΔT = ΔT_{f}  ΔT_{i}
 If the temperature increases, T_{f} > T_{i} and so ΔT > 0 and so q > 0. Increasing the heat, increases the temperature and vice versa.
 If the temperature decreases, T_{f} < T_{i} and so ΔT < 0 and so q < 0. Decreasing the heat, decreases the temperature and vice versa.
 If T_{f} and T_{i} are given in °C, there is no need to convert each to Kelvin as the difference between them is the same on the centigrade and Kelvin scales.
 Whenever you calculate a property from a measurement, the signficant figures must be handled correctly, read the iChem online tutorial (identical to the E9 week 4 prelaboratory information).
What is the final temperature of 12 g of water, initially at a temperature of 25.00 °C, if 125 J of heat is added to it? (The specific heat capacity of water is 4.1813 J g^{1} K^{1}.)
As we are given the mass of water and want to calculate the temperature chsnge:
ΔT = q / (m × c) = (125 J) / (12 g × 4.1813 J g^{1} K^{1}) = 2.5 K or 2.5 °C
The mass is only known to 2 significant figures so the temperature change is also known only to 2 significant figures. Note that as heat is added, q is positive leading to ΔT being positive too.
The initial temperature is 25.00 °C and the temperature increase is positive so the final temperature is (25.00 + 2.5) °C = 27.5 °C
What is the heat change for a 25 g block of aluminium, initially at a temperature of 225 °C, plunged into a large bath of water at 26 °C? (The specific heat capacity of aluminium is 0.897 J g^{1} K^{1}.)
The initial temperature is 225 °C and the final temperature is 26 °C. Hence the temperature change is:
ΔT = T_{f}  T_{i} = (26  225 °C) = 199 °C or 199 K.
As we are given the mass of water and want to calculate the heat chsnge:
q = m × c × ΔT = 25 g × 0.897 J g^{1} K^{1} × 199 K = 4500 J
The mass is only known to 2 significant figures so the heat change is also known only to 2 significant figures. Note that the aluminium cools and heat is lost, ΔT is negative leading to q being negative too.
1500 J of heat are added to a block of copper resulting in its temperature rising by 250 ° C. How many moles of copper are in the block? (The molar heat capacity of copper is 24.47 J mol^{1} K^{1}.)
We are given the heat and temperature changes and want to calculate the amount of copper present. As the number of moles is requested, the molar heat capacity is used:
n = q / (C × ΔT) = (1500 J) / (24.47 J mol^{1} K^{1} ×250 K) = 0.25 mol
The heat and temperature changes are both only known to 2 significant figures (the trailing zeros are not significant) so the number of moles is also known only to 2 significant figures