Question

A system absorbs \[600J\] of energy and does work equivalent to $400J$ of energy. The internal energy change is:
$
  A)1000J \\
  B)200J \\
  C)600J \\
  D)300J \\
$

Answer 1

Hint: To calculate the internal energy change we use the formula $\Delta E = Q + W$ where, $\Delta E$ is the internal energy change and $Q$ is the energy absorbed by the system and $W$work done. We have $Q$ and $W$ so, by putting the values in the formula we can easily calculate the internal energy change. And the work done is negative because the internal energy of the system is proportional to its temperature, internal energy is also a state function. Any change in the internal energy of the system is equal to the difference between its initial and final values.

Complete answer:
The internal energy of a thermodynamic system is the energy contained within it. It is the energy necessary to create or prepare the system in any given internal state. The thermodynamic processes that define the internal energy are transfers of matter, or of energy as heat, and thermodynamic work.
When a cell does work or loses heat, its internal energy decreases. If the amount of work done by a cell is the same as the amount of energy transferred in by heat, or the amount of work performed on a cell matches the amount of energy transferred out by heat, there will be no net change in internal energy.
We know that,
$ \Rightarrow \Delta E = Q + W$
$ \Rightarrow 600 + ( - 400)$
$ \Rightarrow 200J$
So, the correct answer is $B)200J$

Note:
The internal energy is an extensive property: it depends on the size of the system, or on the amount of substance it contains. At any temperature greater than absolute zero, microscopic potential energy and kinetic energy are constantly converted into one another, but the sum remains constant in an isolated system.