Here is a question,

When an ideal gas undergoes an adiabatic change causing a temperature change \(\Delta T\)

(**A**)there is no heat gained or lost by the gas

(**B**)the work done by the gas is equal to change in internal energy

(**C**)the change in internal energy per mole of the gas is \({ C }_{ v }\Delta T\), where \({ C }_{ v }\) is the molar
heat capacity at constant volume.

The given answer is **A** and **C**.

Why is **B** not correct?

Here is why I think so,

Since \(\Delta Q=0\) for adiabatic process, \[0=\Delta U+\Delta W\] \[\Longrightarrow -\Delta U=\Delta W\] \(\therefore \) Work done by the gas is equal to change in internal energy.

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## Comments

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TopNewestWork done is not equal to change in internal energy, you have to consider the signs as well. If internal energy change is positive,work done is negative and vice versa.

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Thanks!

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