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Shown in the figure, an insulated rigid tank is divided into two equal parts by a partition. Initially, one part contains an indeal gas, and the other part is evacuated. The partition is then removed, and the gas expands into the entire tank. At the initial state, the mass of the gas is m= 4.00kg, initial pressure is p1 = 600.00 kPa, initial temperature is T1 = 300.00 K. The gas constant is R = 0.2870 kJ/(kg-K). (The internal energy can be determined by the equation AU=m-cy (T2-T1), where cy= 0.7180 kJ/(kg-K) is the specific heat at the constant volume.) Calculate the final state temperature T2. Ideal gas FOSE T1 P1 V1 m State 1 Evacuated (K) Ideal gas T2=? P2=? V2=2V1 State 2

Shown in the figure, an insulated rigid tank is divided into two equal parts by a partition. Initially, one part contains an indeal gas, and the other part is evacuated. The partition is then removed, and the gas expands into the entire tank. At the initial state, the mass of the gas is m= 4.00kg, initial pressure is p1 = 600.00 kPa, initial temperature is T1 = 300.00 K. The gas constant is R = 0.2870 kJ/(kg-K). (The internal energy can be determined by the equation AU=m-cy (T2-T1), where cy= 0.7180 kJ/(kg-K) is the specific heat at the constant volume.) Calculate the final state temperature T2. Ideal gas FOSE T1 P1 V1 m State 1 Evacuated (K) Ideal gas T2=? P2=? V2=2V1 State 2

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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Shown in the figure, an insulated rigid tank is divided into two equal parts by a partition. Initially, one part contains an indeal gas, and the other part is evacuated. The partition is then removed, and the gas expands into the entire tank. At the initial state, the mass of the gas is m= 4.00kg, initial pressure is p1 = 600.00 kPa, initial temperature is T1 = 300.00 K. The gas constant is R = 0.2870 kJ/(kg·K). (The internal energy can be determined by the equation ΔU=m·cv·(T2-T1), where cv =  0.7180 kJ/(kg·K) is the specific heat at the constant volume.) 

Calculate the final state temperature T2.__________ (K)



 

The image describes an insulated rigid tank divided into two equal sections by a partition. Initially, one section contains an ideal gas, while the other section is evacuated. When the partition is removed, the gas expands to fill the entire tank. ### Initial Conditions (State 1): - The gas is classified as an ideal gas. - Temperature \( T1 = 300.00 \) K - Pressure \( P1 = 600.00 \) kPa - Volume \( V1 \) - Mass of gas \( m = 4.00 \) kg ### Gas Constants: - Gas constant \( R = 0.2870 \) kJ/(kg·K) - Specific heat at constant volume \( c_V = 0.7180 \) kJ/(kg·K) ### Final Conditions (State 2): - Ideal gas after expansion - Temperature \( T2 \) is unknown - Pressure \( P2 \) is unknown - Volume \( V2 = 2V1 \) (since it now occupies the entire tank) The relationship for internal energy change is given by \(\Delta U = m \cdot c_V \cdot (T2 - T1)\). ### Task: Calculate the final state temperature \( T2 \). ### Explanation: - The diagram on the left side of the image illustrates **State 1**, showing the ideal gas confined to one half of the tank. - The diagram on the right represents **State 2**, showing the ideal gas now expanded to occupy the full volume of the tank. To find \( T2 \), we apply the energy conservation principles for an ideal gas expanding in an insulated environment. The energy balance equation given, along with the initial conditions, will facilitate solving for the final temperature \( T2 \).
Transcribed Image Text:The image describes an insulated rigid tank divided into two equal sections by a partition. Initially, one section contains an ideal gas, while the other section is evacuated. When the partition is removed, the gas expands to fill the entire tank. ### Initial Conditions (State 1): - The gas is classified as an ideal gas. - Temperature \( T1 = 300.00 \) K - Pressure \( P1 = 600.00 \) kPa - Volume \( V1 \) - Mass of gas \( m = 4.00 \) kg ### Gas Constants: - Gas constant \( R = 0.2870 \) kJ/(kg·K) - Specific heat at constant volume \( c_V = 0.7180 \) kJ/(kg·K) ### Final Conditions (State 2): - Ideal gas after expansion - Temperature \( T2 \) is unknown - Pressure \( P2 \) is unknown - Volume \( V2 = 2V1 \) (since it now occupies the entire tank) The relationship for internal energy change is given by \(\Delta U = m \cdot c_V \cdot (T2 - T1)\). ### Task: Calculate the final state temperature \( T2 \). ### Explanation: - The diagram on the left side of the image illustrates **State 1**, showing the ideal gas confined to one half of the tank. - The diagram on the right represents **State 2**, showing the ideal gas now expanded to occupy the full volume of the tank. To find \( T2 \), we apply the energy conservation principles for an ideal gas expanding in an insulated environment. The energy balance equation given, along with the initial conditions, will facilitate solving for the final temperature \( T2 \).
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