Specific heat capacity and calorimetry

Thermochemistry is the branch of chemistry that deals with the heat changes that accompany chemical reactions. Within this domain, "specific heat capacity" and "calorimetry" are important concepts that help us understand how substances absorb and release heat. This can affect everything from cooking your food to running an engine. In this explanation, we'll go over these concepts in a detailed but easy-to-understand way.

What is specific heat capacity?

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. It is a property that tells us how much heat energy a certain substance can hold. Every substance has its own specific heat capacity.

The formula used to calculate the specific heat capacity is:

q = mcΔT

• q is the heat energy absorbed or released (in joules).
• m is the mass of the substance (in grams).
• c is the specific heat capacity (in joules per gram per degree Celsius, J/g°C).
• ΔT is the change in temperature (in degrees Celsius).

Example calculation

Suppose a piece of metal weighing 100 grams requires 500 joules of heat to raise its temperature from 20°C to 30°C. We can calculate the specific heat capacity of the metal as follows:

q = 500 J 
m = 100 g 
ΔT = 30°C - 20°C = 10°C 
Using q = mcΔT: 
500 = 100 * c * 10 
c = 500 / (100 * 10) 
c = 0.5 J/g°C

The specific heat capacity of the metal is 0.5 joule/gram°C.

Understanding calorimetry

Calorimetry is the process of measuring the heat of chemical reactions or physical changes. A calorimeter is an instrument used for calorimetry, which measures the heat absorbed or released during a chemical reaction. The basic principle behind calorimetry is the law of conservation of energy which states that energy cannot be created or destroyed, only transferred or transformed from one form to another.

Simple calorimeter

A simple calorimeter can be made from a polystyrene cup, a lid, a thermometer, and a stirrer. The substance under investigation is placed in the calorimeter, and the heat change is monitored by observing the temperature change.

Consider a simple system where a known mass of water absorbs heat. The formula is:

q_water = m_water * c_water * ΔT_water

Similarly, if some other reaction or process emits heat, the relation can be applied as follows:

q_process = m_process * c_process * ΔT_process

Example of calculation using a calorimeter

Suppose we add 10.0 g of substance A to 100.0 g of water in a calorimeter. If the temperature of the water rises from 25.0°C to 35.0°C, calculate the heat change for substance A. Given that the specific heat capacity of water is 4.18 J/g°C.

m_water = 100 g 
c_water = 4.18 J/g°C 
ΔT_water = 35°C - 25°C = 10°C 
Using q_water = m_water * c_water * ΔT_water: 
q_water = 100 * 4.18 * 10 
q_water = 4180 J

Therefore, 4180 joules of heat were absorbed by water. This means that 4180 joules of heat were released by substance A in the reaction.

Advanced concepts: Heat capacity vs. specific heat capacity

While specific heat capacity is the heat required to raise the temperature of 1 gram of a substance by 1°C, heat capacity is a more generalized concept. Heat capacity is the amount of heat required to raise the temperature of an object, independent of its mass. It is expressed in joules per degree Celsius (J/°C).

Relation between heat capacity and specific heat capacity

This relationship can be expressed as follows:

C = mc

• C is the heat capacity (J/°C).
• m is the mass (grams).
• c is the specific heat capacity (J/g°C).

Visual example

The circle above represents water absorbing heat in the calorimeter.

The rectangular shape depicts a basic calorimeter setup.

Real-world applications

In the real world, understanding specific heat capacity and calorimetry can help improve energy efficiency, aid cooking and food preparation, and enhance material selection for engineering applications. For example, it explains why water is so effective for cooling systems because of its high specific heat capacity.

Practice problems

1. Calculate the amount of heat needed to raise the temperature of 50 g of aluminum from 25°C to 60°C. The specific heat capacity of aluminum is 0.897 J/g°C.
2. If 200 grams of water is heated and the temperature rises by 15°C, how much heat will be absorbed by the water? The specific heat capacity of water is 4.18 J/g°C.
3. 690 J of heat is required to raise the temperature of a substance weighing 115 g by 18°C. Calculate its specific heat capacity.

Conclusion

Specific heat capacity and calorimetry are fundamental concepts in thermochemistry that provide insight into energy transfer processes. Whether it is chemical reactions or physical changes, these concepts explain how heat is absorbed and released. By mastering these ideas, students and professionals can better understand and manipulate various chemical and physical processes.

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