Why is the ratio of two extensive quantities always intensive?
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Is this something that we observe that always happens or is there some fundamental reason for two extensive quantities to give an intensive when divided?
thermodynamics soft-question definition
asked 40 mins ago
paokara moupaokara mou
984
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$begingroup$
Is this something that we observe that always happens or is there some fundamental reason for two extensive quantities to give an intensive when divided?
thermodynamics soft-question definition
asked 40 mins ago
paokara moupaokara mou
984
$endgroup$
add a comment |
$begingroup$
Is this something that we observe that always happens or is there some fundamental reason for two extensive quantities to give an intensive when divided?
thermodynamics soft-question definition
asked 40 mins ago
paokara moupaokara mou
984
$endgroup$
Is this something that we observe that always happens or is there some fundamental reason for two extensive quantities to give an intensive when divided?
thermodynamics soft-question definition
thermodynamics soft-question definition
asked 40 mins ago
paokara moupaokara mou
984
asked 40 mins ago
paokara moupaokara mou
984
asked 40 mins ago
paokara moupaokara mou
984
asked 40 mins ago
paokara moupaokara mou
984
asked 40 mins ago
paokara moupaokara mou
984
984
add a comment |
add a comment |
1 Answer
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$begingroup$
It is mainly a mathematical reason. Extensive quantities grow with system size. If two quantities scale in the same way with a variable (in this case system size), it cancels out in the division.
Mini-example: $A$ and $B$ are extensive physical quantities both dependent on $n$. Their ratio is called $C = A / B$. If you scale the system up, $A$ and $B$ grow by a factor of $n$. What happens to $C$?
$frac{A cdot n}{B cdot n} = frac{A}{B}$
$C$ stays the same, irrespective of $n$. Hence, $C$ is intensive. The most common physical example is mass and volume, which scale with system size and still exhibit the same ratio, the density.
answered 31 mins ago
lmrlmr
921518
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1 Answer
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1 Answer
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active
oldest
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$begingroup$
It is mainly a mathematical reason. Extensive quantities grow with system size. If two quantities scale in the same way with a variable (in this case system size), it cancels out in the division.
Mini-example: $A$ and $B$ are extensive physical quantities both dependent on $n$. Their ratio is called $C = A / B$. If you scale the system up, $A$ and $B$ grow by a factor of $n$. What happens to $C$?
$frac{A cdot n}{B cdot n} = frac{A}{B}$
$C$ stays the same, irrespective of $n$. Hence, $C$ is intensive. The most common physical example is mass and volume, which scale with system size and still exhibit the same ratio, the density.
answered 31 mins ago
lmrlmr
921518
$endgroup$
add a comment |
$begingroup$
It is mainly a mathematical reason. Extensive quantities grow with system size. If two quantities scale in the same way with a variable (in this case system size), it cancels out in the division.
Mini-example: $A$ and $B$ are extensive physical quantities both dependent on $n$. Their ratio is called $C = A / B$. If you scale the system up, $A$ and $B$ grow by a factor of $n$. What happens to $C$?
$frac{A cdot n}{B cdot n} = frac{A}{B}$
$C$ stays the same, irrespective of $n$. Hence, $C$ is intensive. The most common physical example is mass and volume, which scale with system size and still exhibit the same ratio, the density.
answered 31 mins ago
lmrlmr
921518
$endgroup$
add a comment |
$begingroup$
It is mainly a mathematical reason. Extensive quantities grow with system size. If two quantities scale in the same way with a variable (in this case system size), it cancels out in the division.
Mini-example: $A$ and $B$ are extensive physical quantities both dependent on $n$. Their ratio is called $C = A / B$. If you scale the system up, $A$ and $B$ grow by a factor of $n$. What happens to $C$?
$frac{A cdot n}{B cdot n} = frac{A}{B}$
$C$ stays the same, irrespective of $n$. Hence, $C$ is intensive. The most common physical example is mass and volume, which scale with system size and still exhibit the same ratio, the density.
answered 31 mins ago
lmrlmr
921518
$endgroup$
It is mainly a mathematical reason. Extensive quantities grow with system size. If two quantities scale in the same way with a variable (in this case system size), it cancels out in the division.
Mini-example: $A$ and $B$ are extensive physical quantities both dependent on $n$. Their ratio is called $C = A / B$. If you scale the system up, $A$ and $B$ grow by a factor of $n$. What happens to $C$?
$frac{A cdot n}{B cdot n} = frac{A}{B}$
$C$ stays the same, irrespective of $n$. Hence, $C$ is intensive. The most common physical example is mass and volume, which scale with system size and still exhibit the same ratio, the density.
answered 31 mins ago
lmrlmr
921518
answered 31 mins ago
lmrlmr
921518
answered 31 mins ago
lmrlmr
921518
answered 31 mins ago
lmrlmr
921518
921518
add a comment |
add a comment |
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