What is specific heat capacity?
Energy or heat energy can also be involved in changing the temperature of a substance. Although it is not essential to know more about what temperature is for this section or lesson, you can review it in this link on temperature if you wish. The relationship between energy and a substance’s temperature is described by the equation below:
Heat Energy =

Mass * Specific Heat * Change in Temperature

1  
Q =  m * c * Δ T 
The letter Q represents heat energy (with units of J or cal), the letter m represents mass (with units of g), the letter c represents specific heat capacity (with units of J/g C or cal/g C), and the symbol Δ T represents change in temperature (with units of C). Change in temperature means final temperature minus initial temperature (T_{f} – T_{i}).
The heat energy, mass, and temperature have all been described before. However, we have not yet discussed the specific heat capacity. It is actually a fancy scientific term for something that is very simple. The specific heat capacity is how much energy a certain substance can absorb. Therefore, each chemical substance has a specific heat capacity number that is unique to only that substance and each phase of that chemical substance. For example the specific heat capacity of liquid water will be different from the specific heat capacity of solid water (ice). In a typical chemistry class or book, they organize these specific heat capacities into a table. Most word problems will require you to look up the specific heat capacity on a table. Here is the link to that specific heat capacity table.
One trick that they can add to specific heat capacity problems is stating the amount of liquid H_{2}O you have in milliliters instead of grams. Since 1 milliliter = 1 gram for liquid H_{2}O you can just take however many milliliters they have and turn it into grams.
VIDEO Specific Heat Capacity Demonstrated Example 1: How much energy is required to heat 500g of liquid H_{2}O from 22 C to 40 C. (Specific Heat Capacity Table).
What information does the problem give you?
Answer:
m = 500 g
T_{i} = 22 C
T_{f} = 40 C
c = 4.18 J/g C liquid H_{2}O
What formula do we use to connect this information?
Q =  m * c * Δ T 
How do we fill in the formula with the information?
Q =  500g * 4.18 J/g C * (40 C – 22 C) 
Simplify
Q =  500g * 4.18 J/g C * (18 C) 
Calculate
500 * 4.18 * 18 = 37620
COMPLETE ANSWER: 37620 J
VIDEO Specific Heat Capacity Demonstrated Example 2: If 34kJ energy is required to heat 620g of a solid substance from 24 C to 72 C what is the specific heat capacity of that substance? (Specific Heat Capacity Table).
What information does the problem give you?
Answer:
Q = 34 kJ —> 34000 J
m = 620 g
T_{i} = 24 C
T_{f} = 72 C
c = ?
What formula do we use to connect this information?
Q =  m * c * Δ T 
How do we fill in the formula with the information?
34000J =  620g * c * (72C – 24C) 
Simplify
34000J =  620g * c * (48C) 
How do we solve for c?
Answer: Divide both sides by 620g and 48C
34000J =  620g * c * 48C 
620g * 48C  620g * 48C 
Cross off 620g and 48C from the right side.
34000J =  620g * c * 48C 
620g * 48C  620g * 48C 
Simplify
34000J =  c 
620g * 48C  1 
How do I do the calculations?
Answer: 34000J / (620g * 48 C) = 1.14 J/g C
34000J =  1.14 J/g C 
620g * 48C  1 
What is the complete answer?
COMPLETE ANSWER: 1.14 J/g C
VIDEO Specific Heat Capacity Demonstrated Example 3: If the temperature of 13ml of liquid H_{2}O starts at 36 C and is heated with 650 J. What will be its final temperature? (Specific Heat Capacity Table).
What information does the problem give you?
Answer:
Q = 650 J
m = 13ml —> 13g
T_{i} = 36 C
T_{f} = ?
c = 4.18 J/g C liquid H_{2}O
What formula do we use to connect this information?
Q =  m * c * Δ T 
How do we fill in the formula with the information?
650 =  13 * 4.18 * (T_{f} – 36) 
Do not try to solve for T_{f}. Solve for (T_{f} – 36) first. To do that divide both sides by 13 and 4.18.
650 =  13 * 4.18 * (T_{f} – 36) 
13 * 4.18  13 * 4.18 
Cross off 13 * 4.18 from the right side.
650 =  13 * 4.18 * (T_{f} – 36) 
13 * 4.18  13 * 4.18 
Simplify
650 =  (T_{f} – 36) 
13 * 4.18 
Calculate —> 650 / (13 * 4.18) = 12
12 =  (T_{f} – 36) 
1 
+ 36 to both sides
12 =  (T_{f} – 36) 
+ 36  + 36 
Cross off the 36 on the right side.
12 =  (T_{f} – 36) 
+ 36  + 36 
Simplify
12 =  T_{f} 
+ 36 
Calculate —> 12 + 36 = 48
48 =  T_{f} 
1 
What is the complete answer?
COMPLETE ANSWER: T_{f }= 48 C
PRACTICE PROBLEMS: Calculate the missing information in the specific heat equation. Use the Specific Heat Capacity Table when needed.
How much energy is required to heat 80g of liquid H_{2}O from 13 C to 57 C.
Answer: 14713 J
How much energy is required to heat 173g of solid iron from 205 C to 439 C.
Answer: 18217 J
If 6.4kJ energy is required to heat 510g of a solid substance from 12 C to 31 C what is the specific heat capacity of that substance?
Answer: 0.29 J/g C
If the temperature of 61ml of liquid H_{2}O starts at 27 C and is heated with 840 J. What will be its final temperature?
Answer: 30.3 C