Answer to Question #197064 in Mechanical Engineering for Moses

Question

A quantity of gas occupies a volume of 0.4M² a pressure of 100KN/M³ and a temperature of 20°C the gas is compressed isothermally to a pressure of 450KN/M² then expanded adiabatically to its intial volume for this quantity of gas determine;

1:the heat transferred during the compression

2:the change of internal energy during the expansion

3:the mass of gas.

Answer 1

$n=\frac{R_1V_1}{RT_1}=\frac{100*10^3*0.4}{8.314*293}=16.42mol$

$v_2=\frac{nRT}{P_2}=\frac{16.4*8.314*293}{450*10^3}=0.08878m^3$

(1) $Q_c=nRT_1\ln(\frac{V_2}{V_1})=16.42*8.314*293\ln(\frac{0.08878}{0.4})$

$=-60210.85kJ$

(2)$\triangle u=\frac{nR(T_3-T_2)}{y-1}$

But $V_3=V_1=0.4$

$P_3=P_2(\frac{V_2}{V_3})^y=450*10^3(\frac{0.8878}{0.4})^{1.4}$

$=54697.78$

$T_3=9.293(\frac{54697*78}{450*10^3})^{\frac{0.4}{1.4}}=160.46$

$\triangle u=\frac{16.42*8.314(160-293)}{1.4-1}=-45391.53kJ$

(3) $PV=mRT=m=\frac{100*0.4}{8.314*293}=0.0164kg$