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The culinary art can be considered a form of applied chemistry - chemistry of foods !
It gave birth to modern chemistry and influenced medicine, metallurgy, physics, art, mysticism, spiritualism, semiotics, and astrology.
Pure chemistry refers to pure research - just trying to figure out the properties of existing matter. Applied chemistry means you are using scientific knowledge of chemistry in order to solve a human problem. For example, chemical medicines are an example of applied chemistry.
The branch of chemistry that is being applied in measuring the concentration of an air pollutant is analytical chemistry. It studies the identification, separation, and quantification of the chemical components of nature.
Exaggerating a little we can say that metallurgy is the metals chemistry and processing.
Metallurgy and chemistry
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Paul Smeeton Hunter has written: 'An index to computer-produced standard interest profiles in chemistry, applied chemistry, chemical engineering and metallurgy' -- subject(s): Abstracting and indexing, Abstracting and indexing services, Chemistry, Information storage and retrieval systems
Applied
Carbonates are studied in chemistry. People do PhDs in this field. They are particularly studied in extractive metallurgy and geology.
Walter Curlook has written: 'Pyrometallurgy' -- subject(s): Congresses, Pyrometallurgy, Roasting (Metallurgy), Metallurgy, Extraction (Chemistry)
Applied Organometallic Chemistry was created in 1987.
Organic, inorganic, analytical, physical, and your guess is as good as mine. Biochemistry? Polymer chemistry? Surface chemistry? Theoretical chemistry? Nuclear chemistry? Depending on your bias any of those might be regarded as a subdivision of one of the Big Four or as a largely independent field of study. According to my textbook (Grade 11 Chem) they are Organic, Inorganic, Analytical, Physical and Biochemistry.
chemistry, metallurgy, physics, medicine, astrology, semiotics, mysticism, and art
Vivian B. Lewes has written: 'Service chemistry' -- subject(s): Technical Chemistry, Metallurgy
Applied chemistry is simply the application of theories and principles of chemistry to practical purposes. This is a logical step to choose after studying chemistry.