A system has internal energy `U_1`. If 500 J of heat is supplied to it and at the same time it does 300 J of work. Calculate the internal energy of the system in the new state,

Explanation

To find the internal energy of the system in the new state after supplying heat and doing work, we can use the first law of thermodynamics. The first law states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W).

Let's break down the solution step by step:

### Step 1: Identify the given values
- Initial internal energy of the system: \( U_1 \)
- Heat supplied to the system: \( Q = 500 \, \text{J} \)
- Work done by the system: \( W = 300 \, \text{J} \)
...