One mole of an ideal monatomic gas (intial temperature `T_(0)`) is made to go through the cycle abca as shown in the figure. If U denotes the internal energy, then choose the correct alternatives

Options

A. `U_(c)-U_(a)=10.5RT_(0)`
B. `U_(b)-U_(a)=+4RT_(0)`
C. `W_(crarra)=-3P_(0)V_(0)`
D. `U_(c)gtU_(b)gtU_(a)`

Explanation

(a) `U_(c)-U_(a)=nC_(v)dT=(1)(3R)/(2)(8T_(0)-T_(0))=(21)/(2)RT_(0)`
(b) `U_(b)-U_(a)=nC_(v)dT`
`=(1)(3R)/(2)(3T_(0)-T_(0))=4.5RT_(0)` (wrong)
(c) `W_(crarra)` cannot be determined, but
`|W_(crarra)|gt|W_(ararrb|`
`|W_(crarra)|gt3P_(0)V_(0)'` Hence (C) is wrong