A diatomic ideal gas undergoes a thermodynamic change according to the P-V diagram shown in the figure. Tha total heat given to the gas is nearly (use ln 2 = `0.7`)

Options

A. `2.5 P_(0)V_(0)`
B. `1.4 P_(0)V_(0)`
C. `3.9 P_(0)V_(0)`
D. `1.1 P_(0)V_(0)`

Answer

C

Explanation

`Q_(AB)=DeltaU_(AB)+W_(AB)`
`W_(AB)=0`
`DeltaU_(AB)=f/2 n R Delta T=f/2 (DeltaPV)`
`DeltaU_(AB)=5/2 (DeltaPV)`
`Q_(AB)=2.5 P_(0)V_(0)`
Process `BC, BC`
`Q_(BC)=DeltaU_(BC)+W_(BC)`
`Q_(BC)=0+2P_(0)V_(0)ln2=1.4 P_(9)V_(0)`
`Q_("net")=Q_(AB)+Q_(BC)=3.9 P_(0)V_(0)`