Answer to Question #192685 in Mechanical Engineering for blessing

Question

A cylinder that contains 0.064 kg of carbon dioxide (with molar mass 44 kg/kmol), occupying a volume of 0.025 m3 at 1.1 bar, is compressed reversibly until the pressure is 1.9 bar. Calculate the final temperature, the work done on the C02, and the heat supplied when the process is isothermal

Answer 1

Mass(m)=0.064 kg

Molar mass (M) = 44 kg/ mol

Initial Volume(V₁) =0.025 m³

Initial pressure(P₁)= 1.1 ×10⁵ Pa

Final pressure (p₂)=1.9×10⁵ Pa

Gas constant(R)=Universal gas constant/M=8.31x1000/44

R=188.88 J/kg-K

Assuming co₂ as an ideal gas

$\frac{P_1×V_1}{T_1}=\frac{P_2×V_2}{T_2}=mR$

Since process is isothermal

$T_1=T_2$

$V_2=\frac{P_1×V_1}{p_2}=0.0145 m^3$

$T_2=\frac{P_2×V_2}{mR}=227 K$

Work done(W) is given by

$W=P_1×V_1×ln\frac{V_2}{V_1}=-1494.76 J$

Q=W=-1494.76J