Question

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

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

Answer 1

Answer: (B)

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