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

Options

A. `U_(C ) gt U_(b) gt U_(a)`
B. `U_(C ) - U_(b) = 3 RT_(0)`
C. `U_(c) - U_(a) = (9 RT_(0))/(2)`
D. `U_(b) - U_(a) = (3 RT_(0))/(2)`

Answer

A, B, C, D

Explanation

One mole of an ideal monatomic gas `(` initial temperature `T_(0))` is made to go through cylce `abca` shown in figure. `U` denotes the internal energy.
For the process `ab, (P_(0)V_(0))/( T_(0))=(2P_(0)V_(0))/(T_(0))`
`T_(b)=2T_(0)`
`T_(b)gtT_(a)impliesU_(b)gt U_(a)`
`U_(b)-U_(a)=C, DeltaT=(3R)/( 2) (2T_(0)-T_(0))=(3RT_(0))/(2)`
For the process `bc`,

`U_(b)-U_(a)=(3R)/(2) (4T_(0)-2T_(0))=3RT_(0)`
For the process `ca`, `U_(c)-U_(a)=(3R)/(2)(4T_(0)-T_(0))=(9RT)/( 2)`