Question

A system is provided with $200cal$ of heat and the work done by the system on the surrounding is $40J$. Then its internal energy
(A) Increases by $600J$
(B) Decreases by $800J$
(C) Increases by $800J$
(D) Decreases by $600J$

Answer 1

Hint: To solve this we have to use the first law of thermodynamics which will give a relation between heat, work done by the system on the surrounding and the internal energy of the system. We know two of the parameters and by outing that in the formula given by the first law we can find the value of the third one that is our internal energy.

Complete step by step answer:
First law thermodynamics states that the internal energy is equal to the difference of the heat transfer and the work done by the system. It also states that the energy of the universe will remain the same though it may get exchanged between the system and the surrounding. It basically shows the relation between the change in energy states due to work and the heat transfer.
We know,
$\Delta Q = 200\,cal \times 4.2 = 840J$
$\Delta W = 40J$
Now using first law of thermodynamics we can write,
$\Delta Q = \Delta U + \Delta W$
Where,
$\Delta Q$ is the heat transfer.
$\Delta U$ is the internal energy.
$\Delta W$ is the work done by the system.
Now putting the known values we will get,
$840J = \Delta U + 40J$
$ \Rightarrow 840J - 40J = \Delta U$
Hence the internal energy of the system increases by $800J$.
Therefore the correct option is (C).

Note: Remember that the first law of thermodynamics is an expression of the principle of conservation of energy that states that energy can be transferred from one form to another but cannot be created or destroyed by the system. The most common application of this law is the heat engine.