A closed, rigid tank is filled with a gas modeled as an ideal gas, initially at 60°C and a gage pressure of 300 kPa. The gas is heated, and the gage pressure at the final state is 600 kPa. The local atmospheric pressure is 1 atm. Determine the final temperature, in °C.

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muhammadalambsmathf1 muhammadalambsmathf1 · Answer 1 · 2020-04-09T02:57:26+02:00

Answer:

The final temperature is 225.205 °C

Explanation:

We have given

[tex]T_{1}[/tex] = 60 °C = 333.15 K Initial temperature

[tex]P_{gage}[/tex] = 300 kPa , gage initial pressure ,

[tex]P_{gage2}[/tex] = 600 kPa , gage final pressure ,

[tex]P_{\alpha }[/tex] = 101.325 kPa

[tex]P_{1}[/tex] = [tex]P_{gage} + P_{\alpha }[/tex]

[tex]P_{1}[/tex] = [tex]300 kPa + 1 atm (101.325 kPa/1atm)[/tex]

[tex]P_{1}[/tex] = 401.299 kPa.

And

[tex]P_{2 } = P_{gage 2}+ P_{\alpha }[/tex]

[tex]P_{2 } = 600 kPa + 1 atm ( 101.325 kPa/1 atm)[/tex]

[tex]P_{2 } =[/tex] 600. 299 kPa

So according to ideal gas Model

[tex]P_{ 1} V_{1} = ( R^{-} /m )T_{1}[/tex] this is equation one

[tex]P_{ 2} V_{2} = ( R^{-} /m )T_{2}[/tex] this is equation two

so By dividing equation two with equation one we get

[tex]T_{1} /P_{1} = T_{2} /P_{2}[/tex]

putting values we get

[tex]333.15K/401.299 kPa = T_{2}/600.299 kPa[/tex]

[tex]T_{2}= 498.355 K[/tex] = 225.205 °C

This is final temperature