Physics 132-1 Test 1


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Questions (8 pts. apiece) Answer in complete, well-written sentences WITHIN the spaces provided.

  1. Recall the heating curve of a substance as heat is added to it. If there are regions on the heating curve where the temperature is constant, what is happening to the added heat in those regions?

  2. When we measured the latent heat of vaporization of liquid nitrogen we used a resistor immersed in the liquid as the heat source. We took some data with the current in the resistor turned off. Why?

  3. Boyle's Law states that $PV = constant$ for a gas. Why should you believe this?

  4. We measured the specific heat of aluminum $c_{Al}$ by mixing a known amount hot ( $\approx 100^\circ \rm C$) aluminum pellets with a known amount of cold water and recording the final temperature of the mixture. The measured values of $c_{Al}$ differed from the accepted value by about 10%. What are some possible sources of error?

  5. Recall our analysis of a one-atom gas. Starting from Newton's Second Law show the force exerted on a wall is

    \begin{displaymath} F_x = 2m \frac{v_x}{\Delta t_x} \end{displaymath}

    where $m$ is the mass of the particle, $\Delta t_x$ is the time interval between collisions with the wall, and $v_x$ is the component of the velocity perpendicular to the wall. Clearly show all steps for full credit.

  6. Consider the set of data below which has an average and standard deviation of $1.508\pm 0.015$. Our theoretical prediction from kinetic theory is $C_V/N_A k_B = 1.5$. Do the data support that prediction? Why or why not? Be quantitative in your answer.



    Atom \( \frac{C_{V}}{N_{A}k_{B}} \)
    Xe 1.53
    Ar 1.50
    Ne 1.51
    Kr 1.49





Problems. Clearly show all reasoning for full credit. Use a separate sheet to show your work.

1. 15 pts. A vessel of volume $V= 4\times 10^{-3}~m^3$ contains $N=10^{24}$ molecules of nitrogen gas at a pressure $P = 8\times 10^5~N/m^2$. What is the average translational kinetic energy of each molecule?

2. 17 pts. What is the work done by a fluid that expands from $A$ to $B$ as shown in the figure.



\includegraphics[]{fig1.eps}




3. 20 pts. What mass of steam at $T_0 = 100^\circ C$ must be mixed with a mass $m_1 = 0.20~kg$ of ice at its melting point in a thermally insulated container to produce liquid water at $T_1 = 60^\circ C$?










Some constants.

$T_{boiling}$ (water) $373~K$ or $100^\circ\rm C$ $T_{freezing}$ (water) $273~K$ or $0^\circ\rm C$
$L_v$(water) $2.26\times 10^6~J/kg$ $L_f$ (water) $3.33\times 10^5~J/kg$
$c$ (water) $4.19\times 10^3~J/kg-K$ $c$ (steam) $0.69~J/kg-K$
$\rho$ (water) $1.0\times 10^3 kg/m^3$ $P_{atm}$ $1.05\times 10^5 ~N/m^2$
$k_B$ $1.38\times 10^{-23}~J/K$ proton/neutron mass $1.67\times 10^{-27}~kg$
$R$ $8.31J/K-mole$ $g$ $9.8~m/s^2$
$0~K$ $\rm -273^\circ~C$ $1 ~ u$ $1.67\times 10^{-27}~kg$
Gravitation constant $6.67 \times 10^{-11}~N-m^2/kg^2$ Earth's radius $6.37\times 10^6~m$

Physics 132-3, Study Sheet


Test 1



\begin{displaymath} P = {\vert\vec F\vert \over A} \qquad PV = Nk_B T = nRT \qquad F_g = mg \qquad \end{displaymath}


\begin{displaymath} Q = C\Delta T = cm\Delta T = n C_v \Delta T \qquad Q_{f,v} = m L_{f,v} \end{displaymath}


\begin{displaymath} \Delta E_{int} = Q-W \qquad W = \int_a^b \vec F \cdot d\vec ... ..._b} P dV \rightarrow P\Delta V \qquad W = F_{constant}d \qquad \end{displaymath}


\begin{displaymath} \vec F = m \vec a = {d\vec p \over dt} \qquad \langle \vec F... ...gle = {\Delta \vec p \over \Delta t} \qquad P = P_0 + \rho g h \end{displaymath}


\begin{displaymath} KE = {1 \over 2} mv^2 \qquad ME_0 = ME_1 \qquad \vec p = m \vec v \qquad \vec p_0 = \vec p_1 \qquad \end{displaymath}


\begin{displaymath} \overline {KE} = \langle E_{kin} \rangle = {1 \over 2}m \o... ...qquad E_{int} = N ~ \langle E_{kin} \rangle = {3\over 2} Nk_BT \end{displaymath}


\begin{displaymath} v_{rms} = \sqrt{\overline {v^2} } \qquad C_{V} = {f\over 2} ... ...\qquad E_f = { k_BT \over 2} \qquad E_{int} = {f\over 2} Nk_BT \end{displaymath}

f $\equiv$ number of degrees of freedom


\begin{displaymath} {d \over dx} x^n = nx^{n-1} \qquad \int x^n dx = {x^{n+1} \over n+1} + c \end{displaymath}


\begin{displaymath} \langle x\rangle = \frac{1}{N}\sum_i x_{i} \qquad \sigma = \... ...um_i \left( x_{i}-\left\langle x\right\rangle \right)^2}{N-1}} \end{displaymath}


\begin{displaymath} A = 4\pi r^2 \qquad V = Ah \qquad V = {4\over 3} \pi r^3 \end{displaymath}