Question

Given that $1g$ of water in liquid phase has volume $1c{m^3}$ and in vapour phase $1671c{m^3}$ at atmospheric pressure and the latent heat of vaporization of water is $2256J/g$; the change in the internal energy in Joules for $1g$ of water at $373K$ when it changes from liquid phase to vapour phase at the same temperature is $L\;$:
A) 2256
B) 67
C) 2089
D) 1

Answer 1

Hint
From the first law of thermodynamics we know that$\Delta Q = \Delta U + \Delta W$. Substitute work done as$\Delta W = P\Delta V$. Now put the corresponding values and simplify to calculate the change in internal energy.

Complete step-by-step answer
The first law of thermodynamics is based on the conversion of energy.
According to the first law of thermodynamics, heat given to a system $(\Delta Q)$ of medium is equal to the sum of increase in its internal energy $(\Delta U)$ and the work done $(\Delta W)$ by the system against the surroundings.
It is given by,
$\Delta Q = \Delta U + \Delta W$
Given:
$\Delta Q = 2256J/g$
$P = {10^5}Pa$
$\Delta V = 1671 - 1 = 1670c{m^3}$
We know that,
$\Delta W = P\Delta V$
Substitute the known data in the expression,
$2256 = \Delta U + {10^5} \times 1670 \times {10^{ - 6}}$
$\Delta U = 2256 - 167$
$\Delta U = 2089J$
Hence, the change in internal energy is $\Delta U = 2089J$.
The correct option is C.

Note
One can go wrong while writing the first Law of Thermodynamics. In Physics it is $\Delta Q = \Delta U + \Delta W $ but in Chemistry it is written as $\Delta Q = \Delta U - \Delta W$. These differ because of the point of reference. In Physics we are looking at the system from outside. Hence $\Delta W$ is the work done on the system. While in Chemistry $\Delta W$ is the work done by the system. Do take care of this distinction in the convention.
Limitation of the first law of thermodynamics is that it does not indicate the direction of heat transfer. It does not tell about the conditions under which heat can be transformed into work and also doesn’t tell why the heat energy cannot be converted into mechanical energy continuously.