SATHEE: Thermodynamics Question 11

Thermodynamics Question 11

Question: Pressure-temperature relationship for an ideal gas undergoing adiabatic change is $(γ = C_{p} / C_{v})$

[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 = $γ \times$ adiabatic curve slope

C) Adiabatic curve slope = $γ \times$ isothermal curve slope

D) Adiabatic curve slope = $\frac{1}{2} \times$ isothermal curve slope

Show Answer

Answer:

Correct Answer: C

Solution:

For Isothermal process $P V =$ constant $\Rightarrow (\frac{d P}{d V}) = \frac{- P}{V} =$ Slope of Isothermal curve

For adiabatic $P V^{γ} =$ constant $\Rightarrow \frac{d P}{d V} = \frac{- γ P}{V} =$ Slop of adiabatic curve slope

Clearly, ${\frac{d P}{d V}}_{adiabatic} = γ {\frac{d P}{d V}}_{Isothermal}$

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Thermodynamics Question 11

Question: Pressure-temperature relationship for an ideal gas undergoing adiabatic change is (γ=Cp/Cv)

Options:

Answer:

Solution:

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Question: Pressure-temperature relationship for an ideal gas undergoing adiabatic change is $(γ = C_{p} / C_{v})$