The slope of adiabatic (ks) and isothermal (kt) curves related as:
Correct answer: A. Ks=ℽkt
- A. Ks=ℽkt
- B. Ks=kt/ℽ
- C. ks= kt
- D. ks=2kt
Explanation
An isothermal process has pV constant, and the derivative of this with respect to V gives dp/dV = -p/V , while for adiabatic, pVℽ is constant and the derivative of this with respect to V gives dp/dV = -pℽ/V , hence equating these proves option A.For an ideal gas, the adiabatic bulk modulus Ks is given by:Ks = γP,where P is the pressure of the gas.The isothermal bulk modulus kt is given by:kt = P,where P is the pressure of the gas.Substituting these expressions into the equation above, we get:γP = γktSimplifying, we get:Ks = γktTherefore, the slope of an adiabatic curve and the slope of an isothermal curve for an ideal gas are related by Ks = γkt. This relationship is useful in thermodynamics and fluid dynamics for analyzing the behavior of gasses undergoing adiabatic and isothermal processes.
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