Thermodynamic statements Question 13 from [1, p. 4.2]:


  Which of the following statements is true?
  
  (a) An ideal gas always obeys the equation: $PV^γ = \mathrm{constant}$ in adiabatic process. 
  
  (b) An ideal gas always obeys the equation: $PV^x = \mathrm{constant}$ in
  polytropic process.   
  
  (c) In a polytropic process, the heat capacity of the system remains same
  throughout.  
  
  (d) In all the cyclic process, $w_\mathrm{net}$ by the system is non-zero.


To me (a), (b) and (c) appear to be correct, but the solution manual says only the (c) is right. 

References


Neeraj, K. Advanced Problem in Physical Chemistry for Competitive Examinations, 2nd ed.; Pearson India Education Services Pvt. Ltd: Dehli, Chennai, 2015. ISBN 978-93-325-4373-7.
(a) is not true, because, in addition to being adiabatic, the process must be reversible.

(b) is not true, because the gas must be assumed to have constant heat capacity for this equation to apply