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Home » Pressure-temperature relationship for an ideal gas undergoing adiabatic change is:     A constant B constant c constant D constant
Pressure-temperature relationship for an ideal gas undergoing adiabatic change is:

    \[\gamma=C_{\mathrm{p}} / C_{\mathrm{v}}\]


A \quad \mathrm{PT}^{\top}= constant
B \mathrm{PT}^{-1+\gamma}= constant
c \quad \mathrm{PT}^{-1} \mathrm{~T}^{7}= constant
D \quad \mathrm{P}^{1-\mathrm{T}^{7}}= constant
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Pressure-temperature relationship for an ideal gas undergoing adiabatic change is:

    \[\gamma=C_{\mathrm{p}} / C_{\mathrm{v}}\]


A \quad \mathrm{PT}^{\top}= constant
B \mathrm{PT}^{-1+\gamma}= constant
c \quad \mathrm{PT}^{-1} \mathrm{~T}^{7}= constant
D \quad \mathrm{P}^{1-\mathrm{T}^{7}}= constant

Correct option is
D \mathrm{P}^{1-\mathrm{T}^{7}}= constant
From the first law of thermodynamics, d U=d Q+d W
But for adiabatic process, \mathrm{dQ}=0

    \[\begin{array}{l} \mathrm{dU}=\mathrm{dW} \\ \mathrm{d} \mathrm{U}=\mathrm{nC}_{r} \mathrm{dT} \\ \mathrm{dW}=-\mathrm{PdV} \\ \mathrm{nC}_{\mathrm{r}} \mathrm{dT}=-\mathrm{PdV} \Rightarrow \mathrm{nCr} \mathrm{d} \mathrm{T}+\mathrm{P} \mathrm{dV}=0 \end{array}\]

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