Question

The slopes of isothermal and adiabatic curves are related as:
(A) Isothermal curve slope = Adiabatic curve slope.
(B) Isothermal curves slope = Yx Adiabatic curve slope.
(C) Adiabatic curve slope = Yx isothermal curve slope.
(D) Adiabatic curve slope = 12x isothermal curve slope.​

Answer 1

Step-by-step explanation:

Push or pull of an object is considered a force. Push and pull come from the objects interacting with one another. Terms like stretch and squeeze can also be used to denote force.

#plss flw me then I'll gave you 20 thanks ❤# ✌☺✌☺

Answer 2

$\begin{gathered}\orange\bigstar\:{\underline{\pink{\boxed{\bf{\gray{(C)\:Adiabatic\:curve\:slope\:=\:\atop{\gamma\times{Isothermal\:curve\:slope}}}}}}}}\:\green\bigstar \\ \end{gathered}$

$\begin{gathered}\Large{\purple{\underline{\textsf{\textbf{Step-by-step\:Explanation\::}}}}} \\ \end{gathered}$

❶ Isᴏ-ᴛʜᴇʀᴍᴀʟ Pʀᴏᴄᴇss :-

• ✯ It is a process that takes place in the system under constant constant temperature.
• ★ The equation that represents this process is,

$➛ \begin{gathered}\bf{P\:V\:=\:C} \\ \end{gathered}$

Wʜᴇʀᴇ,

• P is the pressure.
• V is the volume.
• C is a constant term.
• ↝ Differentiating w.r.t V,

$➛ \begin{gathered}\sf{V\:\dfrac{dP}{dV}\:+\:P\:\dfrac{dV}{dV}\:=\:0} \\ \end{gathered}$

$➛ \begin{gathered}\sf{V\:\dfrac{dP}{dV}\:=\:-\:P\:\dfrac{dV}{dV}\:} \\ \end{gathered}$

$➛ \begin{gathered}\bf\blue{\dfrac{dP}{dV}\:=\:-\:\dfrac{P}{V}\:} \\ \end{gathered}$

$\Large\bf{Therefore,}$

The slope of isothermal process is $\tt{-\dfrac{P}{V}}−$

❷ Aᴅɪᴀʙᴀᴛɪᴄ Pʀᴏᴄᴇss :-

• ✯ It is a process which takes place with zero heat transfer from the system or surroundings.
• ★ The equation that represents this process is,

$➙ \begin{gathered}\bf{P\:V^{\gamma}\:=\:C} \\ \end{gathered}$

Wʜᴇʀᴇ,

• γ is the ratio of specific heat calculated at constant pressure and constant volume.
• ↝ Differentiating w.r.t V,

$➙ \begin{gathered}\sf{V^{\gamma}\:\dfrac{dP}{dV}\:+\:P\:\dfrac{d(V^{\gamma})}{dV}\:=\:0} \\ \end{gathered}$

$➙ \begin{gathered}\sf{V^{\gamma}\:\dfrac{dP}{dV}\:=\:-\:P\:\dfrac{d(V^{\gamma})}{dV}\:} \\ \end{gathered}$

$➙ \begin{gathered}\sf{V^{\gamma}\:\dfrac{dP}{dV}\:=\:-\:P\:{\gamma}\:V^{(\gamma\:-\:1)}\:} \\ \end{gathered}$

$➙ \begin{gathered}\sf{\dfrac{dP}{dV}\:=\:\dfrac{-\:P\:{\gamma}\:V^{(\gamma\:-\:1)}}{V^{\gamma}}\:} \\ \end{gathered}$

$➙ \begin{gathered}\sf{\dfrac{dP}{dV}\:=\:-\:P\:{\gamma}\:V^{(\gamma\:-\:1\:-\:\gamma)}\:} \\ \end{gathered}$

$➙ \begin{gathered}\sf{\dfrac{dP}{dV}\:=\:-\:P\:{\gamma}\:V^{-1}\:} \\ \end{gathered}$

$➙ \begin{gathered}\bf\pink{\dfrac{dP}{dV}\:=\:-\:{\gamma}\:\dfrac{P}{V}\:} \\ \end{gathered}$

$\Large\bf{Therefore,}$

The slope of adiabatic process is $\tt{-\gamma\dfrac{P}{V}}$

Nᴏᴡ,

➣ Comparing the slope, we see that the slope of the adiabatic curve is γ times the slope of the isothermal curve.

Sagar9040~