1. Tardigrade
  2. Question
  3. Physics
  4. If for hydrogen Cp-Cv=m and for nitrogen Cp-Cv= n where, C p and C v refer to specific heat per unit mass respectively at constant pressure and constant volume, the relation between m and n is (molecular weight of hydrogen =2 and molecular weight of nitrogen =28 )

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Q. If for hydrogen $C_{p}-C_{v}=m$ and for nitrogen $C_{p}-C_{v}=$ $n$ where, $C _{ p }$ and $C _{ v }$ refer to specific heat per unit mass respectively at constant pressure and constant volume, the relation between $m$ and $n$ is (molecular weight of hydrogen $=2$ and molecular weight of nitrogen $=28$ )

Thermodynamics

Solution:

For hydrogen,
$C _{ p }- C _{ v }=\frac{ R }{ M _{ H 2}}=\frac{ R }{2},$
but given that $C _{ n }- C _{ v }= m$
$m = R / 2$
For nitrogen, $C_{p}-C_{v}=n$
$\therefore n = R / 28$
$\therefore \frac{ m }{ n }=\frac{ R / 2}{ R / 28}=14$
Hence, $m=14 n$