Specific heat explanation

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It required heat to raise the temperature of a given amount of substance and the quantity of heat depends on the temperature change.

The heat capacity (C) of a sample of substance is the quantity of heat needed to raise the temperature of the sample of substance by one degree celcius. Changing temperature of the sample from an initial temperature t i to final temperature tf requires heat equal to

 q = C delta t

where delta t is the change of temperature and equals   t- t i

Heat capacity is directly proportional to the amount  of substance. Often heat capacities are listed for molar amounts of substances. The molar heat capacity of a substance is its heat capacity for one mole of substance.

Heat capacity are also compared for one-gram amounts of substances.The specific heat capacity or simply specific heat is the quantity of heat required to raise the temperature of one gram of a substance, s, by the mass in grams, m and the temperature change delta t.

 q=  m x s x delta t

the specific heat and molar heat capacities of few substances must be listed  in the book in the form of table

For example;

Q: A piece of iron requires 6.70 J of heat to raise the temperature by one degree celcius. Its heat capacity is therefore 6.70 J/ oc. The quantity of heat required to raise temperature of piece of iron from 25.0 oc to 35.0 oc is 

q = C delta t = 6.70 J/oc x (35.0 oc - 25.0 oc) = 67.0 J

 

Q: Calculate the heat absorbed by 15.0 g of water to raise the temperature from 20.0 oc to 50.0 oc (at constant pressure). The specific heat of water is 4.18 J/(g.oc).

You substitute into the equation;

q = s x m x delta t

the temperatue change is delta t =   tf - t i   = 50.0 oc - 20.0 oc =  + 30.0 oc

therefore,

q = 4.18 J/(g. oc) x 15.0 g x (+30.0 oc = 1.88 x 10 ^3 J