The compressibility k of a substance is defined as the fractional change in volume of that substance for a given changein pressure: k = - 1/V dV/dP(a) Explain why the negative sign in this expression ensures k is always positive. (b) Show that if an ideal gas is compressed isothermally, its compressibility is given by k1 = 1/P. (c) What If? Show that if an ideal gas is compressed adiabatically, its compressibility is given by k2 = 1/(γi). Determine values for (d) k1 and (e) k2 for a monatomic ideal gas at a pressure of 2.00 atm.
The compressibility k of a substance is defined as the fractional change in volume of that substance for a given changein pressure: k = - 1/V dV/dP(a) Explain why the negative sign in this expression ensures k is always positive. (b) Show that if an ideal gas is compressed isothermally, its compressibility is given by k1 = 1/P. (c) What If? Show that if an ideal gas is compressed adiabatically, its compressibility is given by k2 = 1/(γi). Determine values for (d) k1 and (e) k2 for a monatomic ideal gas at a pressure of 2.00 atm.
Chapter3: The First Law Of Thermodynamics
Section: Chapter Questions
Problem 56P: Consider a cylinder with a movable piston containing n moles of an ideal gas. The entire apparatus...
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The compressibility k of a substance is defined as the fractional change in volume of that substance for a given change
in pressure:
k = - 1/V dV/dP
(a) Explain why the negative sign in this expression ensures k is always positive. (b) Show that if an ideal gas is compressed isothermally, its compressibility is given by k1 = 1/P. (c) What If? Show that if an ideal gas is compressed adiabatically, its compressibility is given by k2 = 1/(γi). Determine values for (d) k1 and (e) k2 for a monatomic ideal gas at a pressure of 2.00 atm.
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