Question

A gas at a an initial pressure of 690KN/m3 and temperature of 185 degrees celsius has a mass of 0.45kg. The gas is expanded adiabatically to a final pressure of 138KN/m2 with a fall of temperature of 135 degrees celsius. If the work transfer during the expansion process is 53kj. (a) sketch the p-v diagram. (b) determine, (i) the specific heat capacity at constant volume.(b) the diabatic index.(iii)the specific heat capacity at constant pressure.

Answer 1

(a) sketch the p-v diagram.

(b) determine

(i) the specific heat capacity at constant volume.

$W=mc_v(T_1-T_2) \implies 53000=0.45c_v(185-135) \implies c_v=2355.556J/kg/K$

(ii) the diabatic index.

$\frac{T_2}{T_1}=\frac{P_2}{P_1}^{\frac{\gamma-1}{\gamma}}$

$\frac{408}{458}=\frac{138000}{69000}^{\frac{\gamma-1}{\gamma}}$

$0.8908296=0.2^{\frac{\gamma-1}{\gamma}}$

$Log 0.8908296=Log0.2^{\frac{\gamma-1}{\gamma}}$

$\gamma=\frac{1}{0.928172369}=1.077386$

(iii)the specific heat capacity at constant pressure.

$\frac{C_p}{C_v}= \gamma \implies C_p=2355.556*1.077386 =2537.84 J/kg$