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

MCQ

A gas is allowed to expand in a well insulated container against a constant external pressure of $2.5\ atm$ from an initial volume of $2.50\ L$ to a final volume of $4.50\ L.$ The change in internal energy $\Delta U$ of the gas in joules will be .............. $\mathrm{J}$

A
$-500$
✓
$-505$
C
$+505$
D
$1136.25$

✓

Answer

Correct option: B.

$-505$

b
Work done in Irreversible process

$\mathrm{W}=-\mathrm{P}_{\mathrm{ext}} \Delta \mathrm{V}$

$=-2.5[4.5-2.5]=-5\, \mathrm{L}\; atm$

$=-5 \times 101.3\, \mathrm{J}=-505 \,\mathrm{J}$

Since system is well insulated $q=0$

By First Law of Thermodynamic $\Delta \mathrm{E}=\mathrm{q}+\mathrm{W}$

$\Delta E=W=-505\;J$

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