Question

When 1 moe of ice melts at $0^{o}C$ and at constant pressure of 1 atm, 1440 calories of heat are absorbed by the system. The molar volume of ice and water are 0.0196 and 0.0180 litre respectively. Which of the following is correct?

• A. $\Delta U\approx \Delta H$
• B. $\Delta U=1548cal$
• C. $\Delta U=1056cal$
• D. None of the above

Answer 1

The correct option is A $\Delta U\approx \Delta H$

Given, $p=1atm=76\times 13.6\times 981dynec{m}^{-2}{V}_1=18c{m}^3,V_1=19.6c{m}^3$
Since $\Delta H=q_p$
= heat absorbed by the system at constant pressure
=1440 calories

In the equation, $\Delta H=\Delta U+p\Delta V$
$\Delta H-\Delta U=p\Delta V$
$p\Delta V=1\times (0.018-0.0196)atmL$
$p\Delta V=0.0016\times 101.3J=0.16J$
$p\Delta V=\frac{0.16}{4.2}$ calories
$p\Delta V=-0.038$ calories
Since $p\Delta V$ is very small as compared to $\Delta U$, $p\Delta V$ can be neglected.
Thus, $\Delta H\approx \Delta U=1440$ calories