Question

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.

Answer 1

gauge pressure is 133 kPa

Step-by-step 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 ×
`10^(5)` Pa

P (gauge ) = 2 ×
`10^(5)` Pa

so from idea gas equation

`(P1*V1)/(T1) = (P2*V2)/(T2)` ................1

so
`{P2} = (P1*T2)/(T1)`

`{P2} = (2*10^5*350)/(300)`

P2 = 2.33 ×
`10^(5)` Pa

so gauge pressure = absolute pressure - atmospheric pressure

gauge pressure = 2.33 ×
`10^(5)` - 1.0 ×
`10^(5)`

gauge pressure = 1.33 ×
`10^(5)` Pa

so gauge pressure is 133 kPa