Question

An ideal gas expands against a constant external pressure of 2 atmosphere from 20 litre to 40 litre and absorbs 10KJ of heat from surrounding. What is the change in internal energy of the system?
A. 4052J
B. 5948J
C. 14052J
D. 9940J

Answer 1

Hint:Firstly, you could identify the given process to be endothermic as the heat is being absorbed by the system. Then you could find the work done by the system in the given endothermic process. We could now remember the first law of thermodynamics and then substitute the given values accordingly to get the change in internal energy of the system. Also, take care of the signs while substituting.

Formula used:
Work done,
$w={{P}_{ext}}\Delta V$
First law of thermodynamics,
$\Delta U=q+w$

Complete answer:
In the question, we are given an ideal gas that is undergoing expansion at constant external pressure of 2atm. The gas is getting expanded from an initial volume of 20L to 40L on absorbing 10KJ heat from the surrounding. We are asked to find the internal energy of the system.
As in the given question the heat is being absorbed, we could say that the given process is endothermic. So, the Heat absorbed will be definitely greater than zero, that is, positive. That is,
$q=10kJ=10000J$ ……………………………………. (1)
Now, let us recall the expression for work done which is given by,
$w=-{{P}_{ext}}\Delta V$ ……………………………………. (2)
The external pressure is given as,
${{P}_{ext}}=2atm$ …………………………………… (3)
The change in volume is given by,
$\Delta V={{V}_{2}}-{{V}_{1}}$
As the gas expands from 20L to 40L, the change in volume would be,
$\Delta V=40-20=20J$ ……………………………………. (4)
We could now substitute (3) and (4) in (2), to get,
$w=-2\times 20=-40Latm$ ……………………………………. (5)
But we know that,
$1Latm=101.325J$
So, (5) becomes,
$w=-40\times 101.3J$
$\therefore w=-4052J$ ……………………………………. (6)
Now, from first law of thermodynamics, we know that the change in internal energy is given by,
$\Delta U=q+w$
We could now substitute the values from equations (1) and (6) to get,
$\Delta U=10000-4052$
$\therefore \Delta U=5948J$
Therefore, we found the change in internal energy of the given system to be 5948J.

Hence, option B is found to be the correct answer.

Note:
As we are dealing with an endothermic process, we could say that the work is done by the system. And by convention, we know that when the work is done by the system we say the work done is negative. This is the reason why we have taken the work done to be negative while solving the question.