MCQ
Consider $1 \,kg$ of liquid water undergoing change in phase to water vapour at $100^{\circ} C$. At $100^{\circ} C$, the vapour pressure is $1.01 \times 10^5 \,N - m ^2$ and the latent heat of vaporization is $22.6 \times 10^5 \,Jkg ^{-1}$. The density of liquid water is $10^3 \,kg m ^{-3}$ and that of vapour is $\frac{1}{1.8} \,kg m ^{-3}$. The change in internal energy in this phase change is nearly ............ $\,J kg ^{-1}$
  • A
    $1.8 \times 10^5$
  • $20.8 \times 10^5$
  • C
    $22.6 \times 10^5$
  • D
    $11.3 \times 10^5$

Answer

Correct option: B.
$20.8 \times 10^5$
b
(b)

Change in volume of $1 \,kg$ of water due to phase change is

$\Delta V=V_{\text {steam }}-V_{\text {water }}$

$=\frac{m_{\text {seam }}-m_{\text {water }}}{\rho_{\text {steam }}}-\rho_{\text {water }}$

$=\frac{1}{(1 / 18)}-\frac{1}{1000}$

$=1800-0.001=1799 \,m ^3$

Work done against atmospheric pressure during phase change is

$\Delta W =p \Delta V$

$=101 \times 10^5 \times 1799$

$=181699 \,J$

Heat absorbed during phase change is

$\Delta Q =m L$

$=1 \times 22.6 \times 10^5$

$=2260000 \,J$

So, change in internal energy is

$\Delta U =\Delta Q-\Delta W$

$=2260000-181699$

$=2078301 J \,kg$

$=208 \times 10^5 \,J kg ^{-1}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

A planet has twice the radius but the mean density is $\frac{1}{4}^{th}$ as compared to earth. What is the ratio of escape velocity from earth to that from the planet
A person sitting firmly over a rotating stool has his arms stretched. If he folds his arms, his angular momentum about the axis of rotation:
A rigid lamina is rotating about an axis passing perpendicular to its plane through point $O$ as shown in figure. The angular velocity of point $B$ w.r.t $A$ is ....... $rad/s$.
If the block $A$ & $B$ are moving towards each other with acceleration $a$ and $b$. Find the net acceleration of $C$.
Which of the following is a mechanical wave?
Velocity of sound waves in air is $330\; m/sec$. For a particular sound in air, a path difference of $40 \;cm$ is equivalent to a phase difference of $1.6 \pi$. The frequency of this wave is... $Hz$
The two ends of a metal rod are maintained at temperatures $100 ^o C$ and $110^o C$. The rate of heat flow in the rod is found to be $4.0\ J/s$. If the ends are maintained at temperatures $200^o\  C$ and $210^o\ C$, the rate of heat flow will be.... $J/s$
In an experiment of simple pendulum time period measured was $50\,sec$ for $25$ vibrations when the length of the simple pendulum was taken $100\,cm$ . If the least count of stop watch is $0.1\,sec$ . and that of meter scale is $0.1\,cm$ then maximum possible error in value of $g$ is .......... $\%$
An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are $6.4 \;\mathrm{cm}$ and $4.8 \;\mathrm{cm},$ respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is:
A body weighs $72\; N$ on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth ?