The relation between U, p and V for an ideal gas in an adiabatic process is given by relation `U=a+bpV`. Find the value of adiabatic exponent `(gamma)

Question

The relation between U, p and V for an ideal gas in an adiabatic process is given by relation `U=a+bpV`. Find the value of adiabatic exponent `(gamma)

The relation between U, p and V for an ideal gas in an adiabatic process is given by relation `U=a+bpV`. Find the value of adiabatic exponent `(gamma)` of this gas.
A. `(a+1)/(a)`
B. `(b+1)/(b)`
C. `(b+1)/(a)`
D. `(a)/(b+1)`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - B
`U = a + bPV = a + bnRT`
`implies DeltaU = bnRDeltaT = nC_(v)DeltaT`
`implies C_(v) = bR implies C_(P) = bR + R`
` implies gamma=(C_(p))/( C_(v)) = (bR+R)/(bR) = (b+1)/(b)`

5 views Answered 2023-02-05 15:29