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Quiz 3 (PHYS262, Summer 2001)

August 8, 2001

1
How many of the following statements are true?
1)
The change in the internal energy of a given system is equal to the sum of the heat given to it and the work done by it (i.e. $\Delta E
= Q+W$).
2)
In a constant-pressure (isobaric) process of a given system, the work done by the system is zero.
3)
In an isothermal (constant-temperature) process of an ideal gas, $PV^\gamma = ~\rm constant$ is satisfied. ( $\gamma = C_P/C_V$)
4)
The heat capacity of a given system is independent of the system size.
(a) Only one (b) Only two (c) Only three (d) All four (e) None

2
In Fig. 1 is shown a $P$-$V$ (pressure-volume) diagram of a certain gas undergoing a cyclic process. In one cycle of the cyclic process, how much work is done by the gas? One unit of pressure and volume is respectively $P_0$ and $V_0$ in the graph.

Figure 1: Prob 2
\begin{figure}
\centerline {\psfig{file=Q4-2.eps,
width=0.2\linewidth,angle=0}}\end{figure}

(a) $8 P_0V_0$ (b) $-8 P_0V_0$ (c) $5 P_0V_0$ (d) $-5 P_0V_0$ (e) $13 P_0 V_0$

3
A gas consists of hydrogen atoms (H) and hydrogen molecules ($~\rm H_2$). At certain thermal equilibrium of the gas, the root-mean-square speed of a hydrogen atom is 400 m/s; what would be the root-mean-square speed of a hydrogen molecule in this gas?

(a) 283 m/s (b) 100 m/s (c) 200 m/s (d) 800 m/s (e) None of the above

4
How long does it take a 350 W coffeepot to boil off $0.7\times 10^3
cm^3$ of water initially at $100.0 ~\rm ^o C$. (The density of water is $ 1 ~\rm g/ cm ^3$, the latent heat of vapourisation of water = $2.1\times 10^6 ~\rm J/kg$ and the specific heat of water is $4.2\times 10^3 ~\rm J/kg\cdot ^o C$).

(a) 6.1 min (b) 70 min (c) $3.9\times 10^3 ~\rm min$ (d) 31 min (e) None of the above

5
How many of the following statements are true?
1)
The efficiency of a heat engine is only dependent on the highest temperature and the lowest temperature of a cycle.

2)
A refrigerator can extract heat from the lower-temperature system and convert it completely into mechanical work.

3)
A Carnot engine is an ideal engine with the perfect (100 %) efficiency.

4)
The entropy change in a reversible process is zero.

(a) Only one (b) Only two (c) Only three (d) All four (e) None




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Hyok-Jon Kwon
2001-08-08