KVPY SX SB Exam 2015 Question Paper

[Note : No. of mole of gas is not given, we have assumed no. of mole = 1]
$\mathit{T}=\frac{\mathit{P}\mathit{V}}{\mathit{R}}$
T will be maximum when PV is maximum
$\mathit{T}=\frac{\mathit{P}\mathit{V}}{\mathit{R}}=\frac{\left(4+2\sin \mathit{\theta }\right)\left(4+2\cos \mathit{\theta }\right)}{\mathit{R}}$
As sin θ and cos θ both
can not be equal to 1 for same value of θ
∴T can not be $\frac{36}{\mathit{R}}$
${\mathit{T}}_{\max }$ should be less than $\frac{36}{\mathit{R}}$ curve is above isothermal curve
∴ temp. is more than $\frac{24}{\mathit{R}}$ on the given process
So ${\mathit{T}}_{\max }$ lie between $\frac{24}{\mathit{R}}\mathrm{and}\frac{36}{\mathit{R}}$
only one option is present