Question

why is adiabatic curve more steeper than isotherm curve?

Answer 1

in adiabatic process curve is more steeper , then isothermal process .

actually , steeping nature of curve depends upon , slope of that curve

first of all we find slope of curve in both processes .

case 1 :- isotheramal process
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PV = constant = K
differentiate wrt V
V.dP/dV + P = 0
dP/dV = -P/V
|dP/dV| = P/V

dP/dV is the slope of curve in P-V graph

case 2 :- adiabatic process
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PV^y = constant = K

differentiate wrt V

V^y .dP/dV + yV^(y-1)P = 0
V.dP/dV + yP = 0
dP/dV = -yP/V = y( -P/V)

|dP/dV| = yP/V --------(2)

if we talk about magnitude of slope in both process , then above explanation we can see that ,
|dP/dV|( adiabatic ) = y|dP/dV| ( isothermal)

e.g

magnitude of slope in adiabatic process > magnitude of process in isothermal process

hence, large angle in positive direction of V-axis by adiabatic process then isothermal process .

so, adiabatic is more steeper then isothrmal process .

Answer 2

As γ is always greater than 1, the slope of an adiabatic curve is greater than that of an isothermal curve by a factor of γ.

Explanation:

• The adiabatic curve is steeper than the isothermal curve, in both the processes of expansion and compression.
• To reach a same height in a longer distance means lower slope of the line.
• Hence adiabatic curve is more steeper than isothermal curve.
• Infact, the steepness of adiabatic curve is times steeper than isothermal curve.
• Adiabats and isotherms are always perpendicular to each other.

To Learn More...

1.Why is adiabatic curve more steeper than isotherm curve?​

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