If the work done on the system or by the system is zero, which one of

If the work done on the system or by the system is zero, which one of the following statements for a gas kept at a certain temperature is correct ?

[amp_mcq option1=”Change in internal energy of the system is equal to flow of heat in or out of the system.” option2=”Change in internal energy of the system is less than heat transferred.” option3=”Change in internal energy of the system is more than the heat flow.” option4=”Cannot be determined.” correct=”option1″]

This question was previously asked in

UPSC NDA-2 – 2019

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The first law of thermodynamics states that the change in internal energy of a system ($\Delta U$) is equal to the heat added to the system ($Q$) minus the work done by the system ($W$). This can be written as $\Delta U = Q – W$. The question states that the work done on the system or by the system is zero, meaning $W = 0$. Substituting this into the first law equation gives $\Delta U = Q – 0$, which simplifies to $\Delta U = Q$. Therefore, the change in internal energy of the system is equal to the flow of heat in or out of the system.

– First Law of Thermodynamics: $\Delta U = Q – W$.
– Work done is zero ($W=0$).
– The change in internal energy is directly equal to the heat transfer when no work is done.

This condition ($W=0$) occurs in processes where the volume of the system does not change (isochoric process) or when the system is rigid. Heat flowing into the system increases its internal energy ($Q > 0, \Delta U > 0$), and heat flowing out decreases its internal energy ($Q < 0, \Delta U < 0$).

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