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Question: In a thermodynamic process pressure of a fixed mass of a gas is changed in such a manner that gas re...

In a thermodynamic process pressure of a fixed mass of a gas is changed in such a manner that gas releases 30 J30\,J of heat and 10J10J of work is done on the gas. If the initial internal energy of the gas was 40 J40\,J, what will be the fixed internal energy?
A. 30 J30\,J
B. 20 J20\,J
C. 60 J60\,J
D. 40 J40\,J

Explanation

Solution

First of all let us find out the change in internal energy. This change in internal energy is equal to the difference between the total heat energy and the work done by the system. The work done on the system is mentioned as negative and energy released is mentioned as negative. These all may help you to solve this question.

Complete step by step answer:
The change in internal energy is expressed as
ΔU=Ufinal−Uinitial\Delta U = {U_{final}} - {U_{initial}}
Following the first law of thermodynamics, change in internal energy is equal to the difference of the total heat energy and the work done by the system. This can be expressed mathematically as,
ΔU=Q−W\Delta U = Q - W
Therefore, we can equate both the equations together,
Ufinal−Uinitial=Q−W{U_{final}} - {U_{initial}} = Q - W
As stated in the question, the heat energy has been released from the system.

According to the conventions, the heat energy released is specified as negative and vice-versa.Therefore we can write that,
Q=−QQ = - Q
And the work done is mentioned as work done on the system. As per the conventions, the work done on the system is mentioned as negative. Therefore we can write that,
W=−WW = - W
Hence we can substitute this in the equation that is,
Ufinal−Uinitial=−Q+W{U_{final}} - {U_{initial}} = - Q + W

The value of work done of the gas is given as,
W=10JW = 10J
The heat energy released is given as,
Q=30JQ = 30J
The initial internal energy is given as,
Uinitial=40J{U_{initial}} = 40J
Substituting these values in the equation will give,
Ufinal−40=−30+10{U_{final}} - 40 = - 30 + 10
∴Ufinal=20 J\therefore {U_{final}} = 20\,J

So, the correct answer is option B.

Note: The first law of thermodynamics is defined as a version of the law of conservation of energy. The work done on an object gets converted into the potential energy possessed by the object. Hence, we find the work done by the change in potential energy. Potential energy is always measured relative to some reference point and only the change in potential energy is significant.