Question

Air is heated from 50 F to 200 F in a rigid container with a heat transfer of 500 Btu. Assume that the air behaves as an ideal gas. Determine the volume of air [ft3] if the initial pressure is 2 atm. Also show the process on a P-v state diagram. Use the following temperature conversion: T[R] = T[F] + 460.

Answer 1

`V=68.86ft^3`

Step-by-step explanation:

`T_1` =10°C,
`T_2` =93.33°C

Q=500 btu=527.58 KJ

`P_1= 2atm`

If we assume that air is ideal gas PV=mRT, ΔU=
`mC_v(T_2-T_1)`

Actually this is closed system so work will be zero.

Now fro first law

Q=ΔU=
`mC_v(T_2-T_1)`+W

⇒Q=
`mC_v(T_2-T_1)`

527.58 =
`m* 0.71(200-50)`

m=4.9kg

PV=mRT

`200V=4.9* 0.287* (10+273)`

`V=1.95m^3` (
`V=1m^3=35.31ft^3`)

`V=68.86ft^3`