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

Answer:

$V=68.86ft^3$

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 =$m\times 0.71(200-50)$

m=4.9kg

 PV=mRT

$200V=4.9\times 0.287\times (10+273)$

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

$V=68.86ft^3$