Question

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.

Answer 1

The final temperature is 225.205 °C

Step-by-step explanation:

We have given

`T_(1)` = 60 °C = 333.15 K Initial temperature

`P_(gage)` = 300 kPa , gage initial pressure ,

`P_(gage2)` = 600 kPa , gage final pressure ,

`P_(\alpha )` = 101.325 kPa

`P_(1)` =
`P_(gage) + P_(\alpha )`

`P_(1)` =
`300 kPa + 1 atm (101.325 kPa/1atm)`

`P_(1)` = 401.299 kPa.

And

`P_(2 ) = P_(gage 2)+ P_(\alpha )`

`P_(2 ) = 600 kPa + 1 atm ( 101.325 kPa/1 atm)`

`P_(2 ) =` 600. 299 kPa

So according to ideal gas Model

`P_( 1) V_(1) = ( R^(-) /m )T_(1)` this is equation one

`P_( 2) V_(2) = ( R^(-) /m )T_(2)` this is equation two

so By dividing equation two with equation one we get

`T_(1) /P_(1) = T_(2) /P_(2)`

putting values we get

`333.15K/401.299 kPa = T_(2)/600.299 kPa`

`T_(2)= 498.355 K` = 225.205 °C

This is final temperature