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A closed, rigid tank is filled with a gas modeled as an ideal gas, initially at 27°C and a gage pressure of 300 kPa. If the gas is heated to 77°C, determine the final pressure, expressed as a gage pressure, in kPa. The local atmospheric pressure is 1 atm.

Respuesta :

Answer:

gauge pressure is 133 kPa

Explanation:

given data

initial temperature T1 = 27°C = 300 K

gauge pressure = 300 kPa = 300 × 10³ Pa

atmospheric pressure = 1 atm

final temperature T2 = 77°C = 350 K

to find out

final pressure

solution

we know that gauge pressure is = absolute pressure - atmospheric pressure so

P (gauge ) = 300 × 10³ Pa - 1 × [tex]10^{5}[/tex] Pa

P (gauge ) = 2 × [tex]10^{5}[/tex] Pa

so from idea gas equation

[tex]\frac{P1*V1}{T1} = \frac{P2*V2}{T2}[/tex]   ................1

so [tex] {P2} = \frac{P1*T2}{T1}[/tex]

[tex] {P2} = \frac{2*10^5*350}{300}[/tex]

P2 = 2.33 × [tex]10^{5}[/tex] Pa

so gauge pressure = absolute pressure - atmospheric pressure

gauge pressure = 2.33 × [tex]10^{5}[/tex]  - 1.0 × [tex]10^{5}[/tex]

gauge pressure = 1.33 × [tex]10^{5}[/tex] Pa

so gauge pressure is 133 kPa

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