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The Relation PV = NRT Holds for All Ideal Gases γ\gamma

Question 27

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The relation PV = nRT holds for all ideal gases. The additional relation PV γ\gamma holds for an adiabatic process. The figure below shows two curves: one is an adiabat and one is an isotherm. Each starts at the same pressure and volume. Which statement is correct? (Note: ' \infty ' means 'is proportional to'.)  The relation PV = nRT holds for all ideal gases. The additional relation PV \gamma  holds for an adiabatic process. The figure below shows two curves: one is an adiabat and one is an isotherm. Each starts at the same pressure and volume. Which statement is correct? (Note: ' \infty ' means 'is proportional to'.)    A) Isotherm:  p \propto \frac{1}{V}  ; Adiabat:  p \propto \frac{1}{V}  : A is both an isotherm and an adiabat. B) Isotherm:  p \propto \frac{1}{V^{r}}  ; Adiabat:  p \propto \frac{1}{V}  : B is an isotherm, A is an adiabat. C) Isotherm:  P \propto \frac{1}{V}  ; Adiabat:   : A is an isotherm, B is an adiabat. D) Isotherm:   ; Adiabat:   : B is both an isotherm and an adiabat. E) cannot answer without additional information about the starting temperature.


A) Isotherm: p1Vp \propto \frac{1}{V} ; Adiabat:
p1Vp \propto \frac{1}{V} : A is both an isotherm and an adiabat.
B) Isotherm: p1Vrp \propto \frac{1}{V^{r}} ; Adiabat:
p1Vp \propto \frac{1}{V} : B is an isotherm, A is an adiabat.
C) Isotherm: P1VP \propto \frac{1}{V} ; Adiabat:
 The relation PV = nRT holds for all ideal gases. The additional relation PV \gamma  holds for an adiabatic process. The figure below shows two curves: one is an adiabat and one is an isotherm. Each starts at the same pressure and volume. Which statement is correct? (Note: ' \infty ' means 'is proportional to'.)    A) Isotherm:  p \propto \frac{1}{V}  ; Adiabat:  p \propto \frac{1}{V}  : A is both an isotherm and an adiabat. B) Isotherm:  p \propto \frac{1}{V^{r}}  ; Adiabat:  p \propto \frac{1}{V}  : B is an isotherm, A is an adiabat. C) Isotherm:  P \propto \frac{1}{V}  ; Adiabat:   : A is an isotherm, B is an adiabat. D) Isotherm:   ; Adiabat:   : B is both an isotherm and an adiabat. E) cannot answer without additional information about the starting temperature. : A is an isotherm, B is an adiabat.
D) Isotherm:  The relation PV = nRT holds for all ideal gases. The additional relation PV \gamma  holds for an adiabatic process. The figure below shows two curves: one is an adiabat and one is an isotherm. Each starts at the same pressure and volume. Which statement is correct? (Note: ' \infty ' means 'is proportional to'.)    A) Isotherm:  p \propto \frac{1}{V}  ; Adiabat:  p \propto \frac{1}{V}  : A is both an isotherm and an adiabat. B) Isotherm:  p \propto \frac{1}{V^{r}}  ; Adiabat:  p \propto \frac{1}{V}  : B is an isotherm, A is an adiabat. C) Isotherm:  P \propto \frac{1}{V}  ; Adiabat:   : A is an isotherm, B is an adiabat. D) Isotherm:   ; Adiabat:   : B is both an isotherm and an adiabat. E) cannot answer without additional information about the starting temperature. ; Adiabat:
 The relation PV = nRT holds for all ideal gases. The additional relation PV \gamma  holds for an adiabatic process. The figure below shows two curves: one is an adiabat and one is an isotherm. Each starts at the same pressure and volume. Which statement is correct? (Note: ' \infty ' means 'is proportional to'.)    A) Isotherm:  p \propto \frac{1}{V}  ; Adiabat:  p \propto \frac{1}{V}  : A is both an isotherm and an adiabat. B) Isotherm:  p \propto \frac{1}{V^{r}}  ; Adiabat:  p \propto \frac{1}{V}  : B is an isotherm, A is an adiabat. C) Isotherm:  P \propto \frac{1}{V}  ; Adiabat:   : A is an isotherm, B is an adiabat. D) Isotherm:   ; Adiabat:   : B is both an isotherm and an adiabat. E) cannot answer without additional information about the starting temperature. : B is both an isotherm and an adiabat.
E) cannot answer without additional information about the starting temperature.

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