Three processes compose a thermodynamic cycle shown in the accompanying `P-V`, diagram of an ideal gas.
Process `1 rarr 2` take place at constant temperature, during this process `60 J` of heat enters the system.
Process `2 rarr 3` takes place at constant volume. During this process `40 J` of heat leaves the system.
Process `3 rarr 1` is adiabatic.
What is the change in internal energy of the during process `3 rarr 1`?

Options

A. `- 40 J`
B. `- 20 J`
C. `+ 20 J`
D. `+ 40 J`

Answer

D

Explanation

d. `1 rarr 2` : isothermal, `Delta U_(12) = 0`
`2 rarr 2`: isochoric, `Delta W = 0`
`implies Delta Q_(23) = Delta U_(23) implies - 40 = Delta U_(23)`
For a cyclic process, `Delta U = 0`
`Delta U_(12) + Delta U_(23) + Delta U_(31) = 0`
`0 + (- 40) + Delta U_(31) = 0`
`0 + (-40) + Delta U_(31) = 0`
`Delta U_(31) = + 40 J`