We have to calculate the value of internal energy change (ΔE) for the process.

The **internal energy**(ΔE or ΔU) of a system can be calculated from the **heat **and **work **of the system.

The relationship between internal energy, heat, and work is shown in the following **equation**:

$\overline{){\mathbf{\u2206}}{\mathbf{E}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{q}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{w}}}$

**Where,**

ΔE = internal energy

q = heat

w = work

Sign conventions for heat and work. Heat, q, gained by a system and work, w, done on a system are both positive quantities, corresponding to "deposits" of internal energy into the system. Conversely, heat transferred from the system to the surroundings and work done by the system on the surroundings are both "withdrawals" of internal energy from the system.

Suppose a system receives a “deposit” of 51 J of work from the surroundings and loses a “withdrawal” of 83 J of heat to the surroundings. What is the magnitude and the sign of E for this process?