Question

$1\, g$ of water on evaporation at atmospheric pressure forms $ 1671\,c{{m}^{3}} $ of steam. Heat of vaporisation at this pressure is $ 540\,cal\,{{g}^{-1}} $ . The increase in internal energy is

• A. 250 cal
• B. 500 cal
• C. 1000 cal
• D. 1500 cal

Answer 1

Answer: (B)

$1\, g$ of water
$\Rightarrow 1 cc$ of water Volume of liquid
$=V_{L}=1 c c=10^{-6} \,m ^{3} $ Volume of vapours
$=V_{V}=1671\, cc =1671 \times 10^{-6} \,m ^{3} $
$\Rightarrow \Delta V=V_{V}-V_{L}=1670 \times 10^{-6} \, m ^{3} $
$\Rightarrow W=p \Delta V=10^{5}\left(1670 \times 10^{-6}\right)=167 \,J$
$\Rightarrow W=\frac{167}{4.18} cal =40 \, cal $
Further, $Q=m L $
$\Rightarrow Q=(1 g)\left(540\, cal\, g^{-1}\right)=540 \, cal$
According to first law of thermodynamics
$Q=\Delta U+W$
$\Rightarrow 540=\Delta U+40$
$\Rightarrow \Delta U=500 \, cal$