Three moles of an ideal gas at 300K are isothermally expanded to five times its initial volume and then heated at this constant volume so that the pressure is raised to its initial value before expansion. In the whole process 8314kJ heat is required. Find γ of the gas.

Let P and V be the initial pressure and volume.
P' and V' be the pressure and volume after isothermal expansion. 
Given,
Number of poles, n = 3
Temperature, T = 300K 
Final volume,  
Perfect gas equation for isothermal process, 
              
          
During isothermal expansion, the change in internal energy of the gas is zero.
Therefore the work done by the gas is equal to heat absorbed by gas.
i.e.
 
         
      
Now the gas is heated at constant volume, therefore the process is isochoric.  
The initial and final values of thermodynamic variables (represented by prime and double prime superscripts) during isobaric process are given as, 
        
Gas equation for adiabatic process is, 
                        
     
According to first law of thermodynamics, 
            
For isochoric process,  
Thus, 
             
Total heat absorbed by gas during the process, 
             
           
          
                     
Now,
Ratio of specific heat is,