Question

Consider an ideal gas of 7 moles that is in contact with a thermal reservoir of temperature 475 K. The gas is enclosed in a container that is allowed to expand and contract. If the initial volume of the gas is 0.50 m ³, find the pressure of the gas some time later after the volume has expanded to 1.50 m ³.

Answer 1

(a). The initial pressure is
`5.5*10^(4)\ Pa`

(b). The final pressure is
`1.8*10^(4)\ Pa`

Step-by-step explanation:

Given that,

Number of moles = 7

Temperature = 475 K

Initial volume = 0.50 m³

Expanded volume = 1.50 m³

We need to calculate the initial pressure

Using formula of pressure

`P_(i)=(nRT_(i))/(V_(i))`

Put the value into the formula

`P_(i)=(7*8.31*475)/(0.50)`

`P_(i)=55261.5\ Pa`

`P_(i)=5.5*10^(4)\ Pa`

We need to calculate the final pressure

Using formula of pressure

`P_(f)V_(f)=nRT_(f)`

After expansion,

`(P_(f)V_(f))/(P_(i)V_(i))=(nRT_(f))/(nRT_(i))`

`P_(f)=(T_(f))/(T_(i))*(P_(i)V_(i))/(V_(f))`

Put the value into the formula

For thermal process,

`T_(i)=T_(f)`

`P_(f)=(5.5*10^(4)*0.50)/(1.50)`

`P_(f)=18333.33\ Pa`

`P_(f)=1.8*10^(4)\ Pa`

Hence, (a). The initial pressure is
`5.5*10^(4)\ Pa`

(b). The final pressure is
`1.8*10^(4)\ Pa`