Consider two mathematical curves drawn for the same ideal gas at a temperature of :

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Thermodynamics · Thermodynamics

Problem

Consider two mathematical curves drawn for the same ideal gas at a temperature of

300\,\text{K}

: (i) Curve I is given by

P=\dfrac{8}{V}

(with

P

in atm and

V

in L), while Curve II is given by

P=\dfrac{20}{V^{1.4}}

. Calculate the pressure predicted by each curve at

V=2.0\,\text{L}

. (ii) A laboratory measurement at

V=2.0\,\text{L}

actually gives

P=18\,\text{atm}

. Which of the two theoretical curves more closely matches the experimental value? Justify quantitatively. (iii) From your answer to part (ii), infer whether the gas is more likely undergoing an isothermal or an adiabatic process near

V=2.0\,\text{L}

. State one reason based on the characteristic equation of the chosen curve.

Related theory

Ideal Gas Law
Equation of State
Thermodynamic Processes
The first law of thermodynamics
Thermodynamics
Isothermal and adiabatic processes

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