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This question examines the adiabatic expansion of an ideal gas. a) Write down the Central Equation of Thermodynamics. The heat capacities at constant volume and pressure are defined by: Cp= where Q is the heat supplied to the material and T is the temperature of the material. b) By considering constant volume heating, show that the internal energy of an ideal gas is: U=CvT. Cy= You may assume that U(T=0)=0. e) Show that for an adiabatic process: CydT=-PdV, and derive a similar expression for Cp. d) Using the previous results, show that for a reversible adiabatic process involving an ideal gas: IT AT= P dV 17--Jav-lap --IV-PP (Notice that this equation involves specific heat capacities.) e) Hence prove that an adiabatic expansion of an ideal gas obeys the relationship: PV = constant, and find an expression for in terms of the heat capacities. In a Joule expansion process a gas expands adiabatically into a vacuum from an initial volume Vi to final volume V₂. f) Explain why entropy is not conserved in this process. g) Show that in general the temperature change is V₁₂-V₁ dP h) Evaluate the temperature change for an ideal gas starting at 300K when the volume is doubled in an adiabatic expansion.

This question examines the adiabatic expansion of an ideal gas. a) Write down the Central Equation of Thermodynamics. The heat capacities at constant volume and pressure are defined by: Cp= where Q is the heat supplied to the material and T is the temperature of the material. b) By considering constant volume heating, show that the internal energy of an ideal gas is: U=CvT. Cy= You may assume that U(T=0)=0. e) Show that for an adiabatic process: CydT=-PdV, and derive a similar expression for Cp. d) Using the previous results, show that for a reversible adiabatic process involving an ideal gas: IT AT= P dV 17--Jav-lap --IV-PP (Notice that this equation involves specific heat capacities.) e) Hence prove that an adiabatic expansion of an ideal gas obeys the relationship: PV = constant, and find an expression for in terms of the heat capacities. In a Joule expansion process a gas expands adiabatically into a vacuum from an initial volume Vi to final volume V₂. f) Explain why entropy is not conserved in this process. g) Show that in general the temperature change is V₁₂-V₁ dP h) Evaluate the temperature change for an ideal gas starting at 300K when the volume is doubled in an adiabatic expansion.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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i need the answer to parts f) g) and h) ONLY. thank you

B.2 This question examines the adiabatic expansion of an ideal gas. a) Write down the Central Equation of Thermodynamics. The heat capacities at constant volume and pressure are defined by: aq aq Cy= ¡ Cp= where Q is the heat supplied to the material and T is the temperature of the material. b) By considering constant volume heating, show that the internal energy of an ideal gas is: U=CyT. You may assume that U(T=0) = 0. e) Show that for an adiabatic process: and derive a similar expression for Cp. d) Using the previous results, show that for a reversible adiabatic process involving an ideal gas: dT CydT=-PdV, RT dV - Lav-lap (Notice that this equation involves specific heat capacities.) e) Hence prove that an adiabatic expansion of an ideal gas obeys the relationship: PV = constant, and find an expression for in terms of the heat capacities. In a Joule expansion process a gas expands adiabatically into a vacuum from an initial volume V₁ to final volume V₂. f) Explain why entropy is not conserved in this process, g) Show that in general the temperature change is AT= T = V₁-V [P-T (OP)]. Cv h) Evaluate the temperature change for an ideal gas starting at 300K when the volume is doubled in an adiabatic expansion.
Transcribed Image Text:B.2 This question examines the adiabatic expansion of an ideal gas. a) Write down the Central Equation of Thermodynamics. The heat capacities at constant volume and pressure are defined by: aq aq Cy= ¡ Cp= where Q is the heat supplied to the material and T is the temperature of the material. b) By considering constant volume heating, show that the internal energy of an ideal gas is: U=CyT. You may assume that U(T=0) = 0. e) Show that for an adiabatic process: and derive a similar expression for Cp. d) Using the previous results, show that for a reversible adiabatic process involving an ideal gas: dT CydT=-PdV, RT dV - Lav-lap (Notice that this equation involves specific heat capacities.) e) Hence prove that an adiabatic expansion of an ideal gas obeys the relationship: PV = constant, and find an expression for in terms of the heat capacities. In a Joule expansion process a gas expands adiabatically into a vacuum from an initial volume V₁ to final volume V₂. f) Explain why entropy is not conserved in this process, g) Show that in general the temperature change is AT= T = V₁-V [P-T (OP)]. Cv h) Evaluate the temperature change for an ideal gas starting at 300K when the volume is doubled in an adiabatic expansion.
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