Question

What is the change in internal energy (ΔΕ) of a system when 5 kJ of work is done on the system while it releases 13 kJ of energy to the surroundings?

Answer 1

The change in internal energy (ΔΕ) of a system : -8 kJ

Further explanation  

The laws of thermodynamics 1 state that: energy can be changed but cannot be destroyed or created  

The equation is:  

 $\tt \Delta U=Q+W$

Energy owned by the system is expressed as internal energy (U)  

This internal energy can change if it absorbs heat Q (U> 0), or releases heat (U <0). Or the internal energy can change if the system does work or accepts work (W)  

The sign rules for heat and work are set as follows:  

• The system receives heat, Q +  

• The system releases heat, Q -  

• The system does work, W -  

• the system accepts work, W +  

5 kJ of work is done on the system : W = +5 kJ

releases 13 kJ of energy to the surroundings : Q = -13 kJ

$\tt \Delta E=-13+5=-8~kJ$