Browse & Filter

In the Fig.-2, let $P_2=10\times10^5$Nm$^{-2}$, $P_1=4\times10^5$Nm$^{-2}$, $v_1=2.5$m$^3$kilomole$^{-1}$. Find

1. the temperature $T$,
2. the specific volume $v_2$,
3. the temperature at points $b$ and $d$,
4. the actual volume $V$ at point $a$ if the system consists of 4 kilomoles of hydrogen,
5. the mass of hydrogen.

The $U$-tube in Fig.-1 below, of uniform cross section 1 cm$^2$, contains mercury to the depth shown. The barometric pressure is 750 Torr. The left side of the tube is now closed at the top, and the right side in connected to a good vacuum pump. Assuming that the temperature remains constant answer the following questions.

1. How far does the mercury level fall in the left side?
2. What is final pressure of the trapped air? 

An approximate equation of state of a real gas at moderate
pressures, devised to take into account of the finite size of the
molecules, is $P(v-b)=R\theta$, where $R$ and $b$ are constants.
Show that

\begin{equation*}
\beta = {1/\theta\over 1+bP/(R\theta)}~~,~~~~\chi =
{1/P\over1+bP/(R\theta)}
\end{equation*}

A metal wire of cross-sectional area 0.0085 cm$^2$ under a
tension of 20 N and a temperature of 20$^\circ$C is stretched
between two rigid supports 1.2 m apart. If the temperature is
reduced to 8$^\circ$C, what is the final tension? (Assume that
$\alpha$ and $Y$ remain constant at the values
$1.5\times10^{-5}$K$^{-1}$ and $2.0\times10^9$ N/m$^2$ respectively)

A metal, whose volume expansivity is 5.0$\times10^{-5}$ K$^{-1}$ and isothermal compressibility is $1.2\times10^{-11}$Pa$^{-1}$, is at a pressure of $1\times10^5$ Pa and a temperature of 20$^\circ$C. A thick surrounding cover of invar, of negligible compressibility and expansivity, fit is very snugly.

• [(a)] What will be the final pressure if the temperature is raised to 32$^\circ$C?
• [(b)] If the cover can with stand a maximum pressure of $1.2\times10^8$Pa, what is the highest temperature two which the system may be raised?

For a gas satisfying van de Waals equation
$$
\left(P+{a\over v^2}\right) (v-b) = R\theta
$$
show that the critical temperature $\theta_c$, critical pressure
$P_c$, and the critical volume are given by

$\theta_c =
{8a\over27Rb}~,~~P_c={a\over27b^2}~,~~v_c=3b\,.\,.$

A sphere of radius \(R_1\) has charge uniformly distributed throughout its volume except for a smaller charge-free spherical volume of radius \(R_2 < R_1\) located entirely within the big sphere. Show that the electric field at all points inside the small sphere is a constant.

Zangwill

A conducting spherical shell of radius \(a\) is placed in a uniform field \(vec{E}\). Show that the force tending to separate two halves of the sphere across a diametrical plane perpendicular to \(\vec{E}\) is given by \[ F = \frac{9}{4}\pi \epsilon_0a^2 E^2.\]

Panofsky and Philips

In the table below, a number in the top row represents the
pressure of a gas in the bulb of a constant volume gas thermometer
when the bulb is immersed in the triplet cell. The bottom row
represents the corresponding readings of the pressure when the bulb
is surrounded by a material at constant unknown temperature.
Calculate the ideal gas temperature of this material (use five
significant figures) {Zemansky}

 Is it necessary to convert the

pressures from mm Hg to Pascal?