1.

The ratio of slope of adiabatic to that of an isothermal process is:

Answer»

`(1)/(GAMMA)`
`gamma`
`gamma-1`
None of the above.

Solution :For isothermal process PV=constant DIFFERENTIATING both sides
PdV + VdP =0
`therefore (dP)/(dV) =-(P)/(V)`
Thus, slope of isothermal process `((dP)/(dV))=-PV" ….(i)"`
For ADIABATIC process `PV^(gamma)=` constant differentiating both sides
`P. gamma. V^(gamma-1)+V^(gamma). dP=0`
`(dP)/(dV)=(gamma P)/(V)`
`therefore` slope of adiabatic process `((dP)/(dV))=(-gamma P)/(V)`
Dividing EQN. (ii) and (i)
`("Slope of adiabatic process")/("Slope of isothermal process")=gamma`
Hence, correct choice is (b).


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