A gas does 4.5 J of external work during adiabatic expansion. If its temperature falls by 2 K, then its internal energy will be

Question

A gas does 4.5 J of external work during adiabatic expansion. If its temperature falls by 2 K, then its internal energy will be (A) increased by 4.5 J (B) decreased by 4.5 J (C) decreased by 2.25 J (D) increased by 9.0 J

Tardigrade Admin · Accepted Answer

During adiabatic process, no heat transfer takes place,
So,

d O = 0

From first law of thermodynamics,

d O = d U + d W

\Rightarrow d U = - d W

\Rightarrow d U = - 4.5 J

As, the temperature falls so internal energy will
decrease i.e.

d U = - 4.5 J

Q. A gas does 4.5J of external work during adiabatic expansion. If its temperature falls by 2K, then its internal energy will be

increased by 4.5 J

decreased by 4.5 J

decreased by 2.25 J

increased by 9.0 J

During adiabatic process, no heat transfer takes place, So, dO=0 From first law of thermodynamics, dO=dU+dW ⇒dU=−dW ⇒dU=−4.5J As, the temperature falls so internal energy will decrease i.e. dU=−4.5J

Q. A gas does $4.5 J$ of external work during adiabatic expansion. If its temperature falls by $2 K$ , then its internal energy will be

During adiabatic process, no heat transfer takes place,
So, $d O = 0$
From first law of thermodynamics,
$d O = d U + d W$
$\Rightarrow d U = - d W$
$\Rightarrow d U = - 4.5 J$
As, the temperature falls so internal energy will
decrease i.e. $d U = - 4.5 J$