Figure demonstrates a polytropic process (i.e.`PV^(n)` = constant ) for an ideal gas. The work done by the gas be in the process `AB` is

Options

A. `(15)/(2) P_(0) V_(0)`
B. `(14)/(3)P_(0)V_(0)`
C. `8P_(0)V_(0)`
D. Insufficient information

Answer

B

Explanation

For a polytropic process `PV^(n)` = constant `implies 16 P_(0) V_(0)^(n) = P_(0)(2V_(0))^(n) implies "n"= 4`
Work done =`(P_(1)V_(1) - P_(2)V_(2))/(n-1) = (16P_(0)V_(0)- P_(0)(2V_(0)))/(4-1) = (14)/(3)P_(0)V_(0)`