A gas has molar heat capacity $C=4.5R$  in the process PT= constant. Then the number of degrees of freedom of each molecule in the gas is

Let us take one mole of an ideal gas, the equation of state becomes, $PV=RT\mathrm{...}\left(i\right)$  
We are given, PT = constant $=K\left(say\right) Or P=\frac{K}{T}\mathrm{.........}\left(ii\right)$  
From Eqs, (i) and (ii), $\left(\frac{K}{T}\right)V=RTOrV=\frac{R}{K}{T}^2$  ……..(iii)
$dW=PdV=\left(\frac{K}{T}\right)\frac{2RT}{K}dTOrdw=2RdT$ 
Now using first law of thermodynamics,
$dQ=dU+dW\Rightarrow CdT=C_{V}dT+2RdT$ 
$\Rightarrow C_V=C-2R=4.5R-2R=\frac{5}{2}R$  But we define $C_V=\frac{f}{2}R$ 
Hence, degree of freedom,  $f=5$