Question

A quantity of a certain perfect gas is compressed from an initial state of 0.085 m³ ,1 bar to a final state of 0.034 m³ , 3.9 bar. The specific heat at constant volume is 0.717 kJ/ kg K, and the specific heat at constant pressure is 1.025 kJ/kg K. The observed temperature rise is 146 K. Calculate the specific gas constant R to three decimal places and state the unit.

Answer 1

$V_1 =0.085\ m³\\ V_2= 0.034\ m³\\ P_1 = 1 \ bar\\ P_2 = 3.9\ bar\\ c_v = 0.724\ kJ/kg.K \\∆T = 146\ K$

$nc_v∆T = nRT\ln(\dfrac{V_2}{V_1})$

$R =\dfrac{c_v}{\ln(\frac{p_1}{p_2})} = \dfrac{0.724}{\ln(\frac{3.9}{1})} = 0.532\ kJ/kg.K$