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

Answer 1

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

$$\mathrm{\Delta }U=Q+W$$

Where:

• $\mathrm{\Delta }U$ 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 $119,\text{J}$.