Thermodynamics Question 11
Question: Pressure-temperature relationship for an ideal gas undergoing adiabatic change is $ (\gamma =C _{p}/C _{v}) $
[CPMT 1992; MP PMT 1986, 87, 94, 97; Pb. PET 1998; DCE 2001; MP PET 2001; UPSEAT 1999, 2001; AFMC 2002]
Options:
A) Isothermal curve slope = adiabatic curve slope
B) Isothermal curve slope = $ \gamma \times $ adiabatic curve slope
C) Adiabatic curve slope = $ \gamma \times $ isothermal curve slope
D) Adiabatic curve slope = $ \frac{1}{2}\times $ isothermal curve slope
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Answer:
Correct Answer: C
Solution:
For Isothermal process $ PV= $ constant $ \Rightarrow ( \frac{dP}{dV} )=\frac{-P}{V}= $ Slope of Isothermal curve
For adiabatic$ PV^{\gamma }= $ constant $ \Rightarrow \frac{dP}{dV}=\frac{-\gamma P}{V}= $ Slop of adiabatic curve slope
Clearly, $ { \frac{dP}{dV} _{\text{adiabatic}}}=\gamma { \frac{dP}{dV} _{\text{Isothermal }}} $
