Question

The internal energy change in a system that has absorbed $2{\text{ }}kcal$ of a heat and done $500{\text{j}}$ of work is:
(A) $7900{\text{j}}$
(B) $8900{\text{j}}$
(C) $3400{\text{j}}$
(D) $5400{\text{j}}$

Answer 1

The First Law of Thermodynamics states that energy can be converted from one form to another with the interaction of heat, work and internal energy, but it can not be created nor destroyed, under any circumstances. when energy passes into or out of a system (as work, heat, or matter), the system's internal energy changes in accord with the law of conservation of energy.
$\Delta H = \Delta U + W$

Complete step by step answer:
Mathematically, this is represented as
$\Delta H = \Delta U + W$
where
$\Delta H = {\text{heat exchanged between a system and its surroundings}}$
$\Delta U = {\text{total change in internal energy of a system}}$
$W = {\text{work done by or on the system}}$
Given,
$\Delta H = 2kcal$
As we know that $1{\text{ }}cal = 4.184j$ so,
$\Delta H = 2{\text{kcal}}$
$\Rightarrow \Delta H = 2 \times 1000 \times 4.184{\text{j}}$
$\Rightarrow \Delta H = 8368{\text{j}}$
$\Rightarrow W = 500{\text{j}}$
Using the first thermodynamic law equation
$\Delta H = \Delta U + W$
Substitute the value of $\vartriangle H$ and $W$ in the above equation
$8368{\text{j}} = \Delta U + 500{\text{j}}$
$\Rightarrow \Delta U = 8368{\text{j}} - 500{\text{j}}$
$\Rightarrow \Delta U = 7868{\text{j}}$
So now we check the given option and select the approximate value nearest the answer. After checking the options we can say the value which is given in option (A) $7900{\text{j}}$ is nearest to the $7868{\text{j}}$.

Note:
The internal energy of a system is identified with the random, disordered motion of molecules; the total (internal) energy in a system includes potential and kinetic energy. This is contrast to external energy which is a function of the sample with respect to the outside environment (e.g. kinetic energy if the sample is moving or potential energy if the sample is at a height from the ground etc).
Internal energy includes energy on a microscopic scale
It is the sum of all the microscopic energies such as:
translational kinetic energy.
vibrational and rotational kinetic energy.
potential energy from intermolecular forces.