Question

Find the change in internal energy of the system when a system absorbs $2$ kilocalorie of heat and at the same time does $500$ joules of work.
A.$7900\;{\text{J}}$
B.$8200\;{\text{J}}$
C.$5600\;{\text{J}}$
D.$6400\;{\text{J}}$

Answer 1

In this question, the concept of the first law of thermodynamics is that the heat transfer to the system is equal to the sum of the change in internal energy of the system and the amount of work done.

Complete step by step answer:
We know that the first law of thermodynamic states that energy cannot be created nor be destroyed but it can change from one form of energy to another form of energy. It is also known as the principle of conservation on energy. The Internal energy of the system is a measure of energy within it. The internal energy is an extensive property in nature.
We know that the first law of thermodynamic mathematically can be represented as,
$\Delta Q = \Delta U + \Delta W$
Where we know that,
$\Delta Q$ is the heat exchange between a system and its surroundings.
$\Delta U$ is the total change in internal energy of the system.
$\Delta W$ is the work done on the system or by the system.
We know that one kilocalorie of heat is equal to $4200\;{\text{J}}$ of heat transfer. By using this conversion rate, the given heat transfer can be converted into Joule as,
$\Delta Q = \left( 2 \right)\left( {4200} \right) \\\ = 8400\;{\text{J}} \\\$
So, from the mathematical expression of first law of thermodynamic,
$\Delta Q = \Delta U + \Delta W$
By substituting the value of $\Delta Q$ and $\Delta W$in the mathematical expression we find internal energy as,
$\Delta Q = \Delta U + \Delta W \\\ \Delta U = \Delta Q - \Delta W \\\ \Delta U = 8400 - 500 \\\ \Delta U = 7900\;{\text{J}} \\\$

Therefore, the option A is correct.

Note: If the work is done on the system, then the work done will have a negative sign and if the work is done by the system then the positive sign will be used. Similarly, if the heat is given to the system then we will take positive signs and if heat is extracted from the system then the negative sign will be used.