A gas is allowed to ospand in a well insulated container against … - Vidyadip

MCQ

A gas is allowed to ospand in a well insulated container against a cemstant eternal pressure of $2.5$ atm from an initial volume of $2.50L$ to a final volume of $4.50L$ The change in internal energy in Joule's will he :

A
$-\ 500J$
✓
$-\ 506J$
C
$+\ 505J$
D
$1136.25J$

✓

Answer

Correct option: B.

$-\ 506J$

$\Delta\text{U}=\text{q}+\text{w}$
For adiabatic process $q = 0$
$\therefore\Delta\text{U}=\text{w}=-\text{P}\Delta\text{V}$
$=-2.5\text{ atm}(4.5-2.5\text{L})$
$=-2.5\times2.0\text{ atm}=-5\text{L atm}$
$\Delta\text{U}=-5\times101.3\text{J}=-506.5\text{J}$

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