Calculate the change in internal energy of the system when it absorbs $20 kJ$ of heat from the surrounding and does work equivalent to $50 kJ$

The change in internal energy is given by the expression:

      $∆U=q+w$                (First Law of Thermodynamics)

First law of thermodynamics states that neither energy created nor destroyed.

Given that, $q=20kJ$

Here, $q$ is positive because heat is absorbed in the system

$w=-50kJ$ 

Here, negative sign shows work is done by the system on the surrounding.

$∆U=20kJ+(-50kJ)$

$∆U=20-50 kJ$

$=-30kJ$

The internal energy of the system decreases by $30kJ$