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.
(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"
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