Question

An ideal gas undergoes an isothermal expansion along path AB, adiabatic expansion along BC, isobaric compression along CD, isothermal compression along DE, and adiabatic compression along EA, as shown in the figure. The work done by the gas along the process BC is 10 J. The change in the internal energy along process EA is 16 J. The absolute value of the change in the internal energy along the process CD is ............ J. 

Hint:

In cyclic processes, the algebraic sum of all internal energy changes over a full cycle is zero. For adiabatic paths, internal energy change equals negative of work done.

Answer 1

Correct Answer: 6

Step 1: Recall the first law of thermodynamics. 
\[ \Delta U = Q - W \] The internal energy change over a complete cycle is zero: \[ \sum \Delta U = 0 \] The work done over one complete cycle equals the total heat absorbed: \[ \sum Q = \sum W \]

Step 2: Analyze given processes. 
- For isothermal processes (AB and DE): \(\Delta U = 0\). - For adiabatic processes (BC and EA): \(Q = 0\), hence \(\Delta U = -W\). Given \(W_{BC} = 10\, \text{J}\) ⇒ \(\Delta U_{BC} = -10\, \text{J}\). Also, \(\Delta U_{EA} = +16\, \text{J}\).

Step 3: Apply energy balance over full cycle. 
\[ \Delta U_{BC} + \Delta U_{CD} + \Delta U_{EA} = 0 \] \[ (-10) + \Delta U_{CD} + (16) = 0 \Rightarrow \Delta U_{CD} = -6 \, \text{J} \] Hence, the absolute value of internal energy change: \[ |\Delta U_{CD}| = 6 \, \text{J} \]

Step 4: Conclusion. 
The absolute value of the internal energy change during process CD is \(6\, \text{J}\).