Question

During compression of a spring, the work done is 10KJ and 2KJ escaped to the surroundings as heat. The change in internal energy $\Delta U$ is:
[A] 8
[B] 12
[C] -12
[D] -8

Answer 1

HINT: To solve this, use the definition of change in internal energy in terms of work and heat according to the first law of thermodynamics. Also, remember that when work is done on the system, heat is released but when work is done by the system, heat is absorbed.

COMPLETE STEP BY STEP SOLUTION: To answer this question, firstly let us discuss what internal energy is. From the first law of thermodynamics we get a relation between the internal energy of the system with heat and work. The relation given is-
$\Delta U=q+w$
In the above relation, $\Delta U$ is the change in internal energy of the system and it is a function of temperature and volume. ‘q’ is the heat absorbed or released and ‘w’ is the work done. It is very important for us to remember that when work is done on the system, heat is released i.e. ‘w’ is positive and ‘q’ is negative but when work is done by the system, heat is absorbed thus ‘w’ is negative and ‘q’ is positive. Now, let us see the question given to us where a spring is compressed and the work done on the spring is 10KJ and 2KJ heat is released. Here, ‘q’ will be negative and ‘w’ will be positive. Therefore, putting the values in the relation of internal energy, we will get-
$\Delta U=-2+10\text{ KJ = 8KJ}$

Therefore, the correct answer is option [A] 8

NOTE: The relation given by the first law of thermodynamics can be expressed in different ways for special cases. At constant temperature i.e. in an isothermal process as the internal energy is a function of temperature and volume, it becomes zero. Therefore, we can write that-
0 = q + w i.e. q = -w.
-When no work is done by the system or upon the system i.e. if ‘w’ becomes zero then the internal energy of the system is equal to the heat and the relation becomes $\Delta U=q$. This process will be an isochoric process because we know work is a function of pressure and volume and it will be zero if there is no change in volume i.e. isochoric process.