Answer to Question #277351 in Molecular Physics | Thermodynamics for dandan

Question

For a certain gas, R=0.277 kJ/kg.K and k=1.384. (a) What are the value of cp and cv? (b) what massof this gas would occupy a volume of 0.425 cu m at 517.11 kPa and 26.7°C? (c) if 31.65 kJ are transferred to this gas at constant volume in (b), what are the resulting temperature ans pressure?

Answer 1

a)

$c_p=\frac{kR}{k-1}=0.998~\frac{kJ}{kg\cdot K},$

$c_V=\frac{R}{k-1}=0.721~\frac{kJ}{kg\cdot K},$

b)

$pV=mRT,\implies m=\frac{pV}{RT}=2.647~kg,$

c)

$Q_V=mc_V(T_2-T_1),\implies$

$T_2=T_1+\frac{Q_V}{mc_V}=316~K,$

$\frac{p_1}{T_1}=\frac{p_2}{T_2},\implies$

$p_2=p_1\frac{T_2}{T_1}=545.7~kPa.$