This problem is providing us with the initial pressure and temperature of two moles of nitrogen which are adiabatically expanded to 1 bar. Thus, final temperature, the heat transferred, and the work of the system are required and found to be 311 K, 0 J and 12,026 J, respectively according to:
In thermodynamics, adiabatic processes are characterized by the absence of heat to attain a specific change. In such a way, one can start by calculating the work as follows:
[tex]W=\frac{K(V_f^{1-\gamma} -V_i^{1-\gamma} )}{1-\gamma}[/tex]
Where:
[tex]\gamma=Cp/Cv=1.4\\\\K=PV^{\gamma}\\\\V_i=\frac{2mol*8.314\frac{Pa*m^3}{mol*K}*600K}{10^6Pa} =0.009977m^3\\\\K=10^6Pa(0.009977m^3)^{1.4}=1579.8J\\\\V_f=\sqrt[1.4]{\frac{1579.8Pa*m^3}{10^5Pa} }=0.0517m^3[/tex]
Now, we can calculate the work with:
[tex]W=\frac{1579.8(0.0517^{1-1.4} -0.009977^{1-1.4} )}{1-1.4}=12,026J[/tex]
The heat is clearly 0 J as the process is adiabatic and the temperature comes from the ideal gas equation:
[tex]T_2=\frac{P_2V_2}{nR}\\ \\T_2=\frac{10^5Pa*0.0517m^3}{2mol*8.314\frac{Pa*m^3}{mol*K} }\\ \\T_2=311K[/tex]
Learn more about adiabatic process: https://brainly.com/question/14926413
