Calculate the value of E in joules for a system that loses 31 J of heat and has 150 J of work performed on it by the surroundings

To calculate the value of \( E \) (the internal energy of the system), we can use the first law of thermodynamics, which states:

\[ \Delta U = Q + W \]

Where:

• \( \Delta U \) is the change in internal energy (which we can denote as \( E \)).
• \( Q \) is the heat added to the system (if the system loses heat, \( Q \) will be negative).
• \( W \) is the work done on the system (if work is done on the system, \( W \) is positive).

In this case:

• The system loses 31 J of heat, so \( Q = -31 , \text{J} \).
• The system has 150 J of work performed on it by the surroundings, so \( W = 150 , \text{J} \).

Now we can substitute these values into the equation:

\[ E = Q + W \] \[ E = (-31 , \text{J}) + (150 , \text{J}) \] \[ E = -31 + 150 \] \[ E = 119 , \text{J} \]

Thus, the value of \( E \) is \( 119 , \text{J} \).