If $25.50$ mol of helium gas is at $10\degree\mathrm{C}$ and a gauge pressure of $0.350$ atm, calculate (a) the volume of the helium gas under these conditions, and (b) the temperature if the gas is compressed to precisely half the volume at a gauge pressure of $1.00$ atm.

A brass plug is to be placed in a ring made of iron. At $15^{\circ} \mathrm{C}$, the diameter of the plug is $8.756 \mathrm{~cm}$ and that of the inside of the ring is $8.742 \mathrm{~cm}$. They must both be brought to what common temperature in order to fit?

A hunk of aluminum is completely covered with a gold shell to form an ingot of weight $45.0 \mathrm{~N}$. When you suspend the ingot from a spring balance and submerge the ingot in water, the balance reads $39.0 \mathrm{~N}$. What is the weight of the gold in the shell?

A brass plug is to be placed in a ring made of iron. At $15^{\circ} \mathrm{C}$, the diameter of the plug is $8.753 \mathrm{~cm}$ and that of the inside of the ring is $8.743 \mathrm{~cm}$. They must both be brought to what common temperature in order to fit? $(b)$ What if the plug were iron and the ring brass?

If 18.75 mol of helium gas is at $10.0^{\circ} \mathrm{C}$ and a gauge pressure of 0.350 atm, calculate the volume of the helium gas under these conditions.

The rms speed of molecules in a gas at $20.0^{\circ} \mathrm{C}$ is to be increased by $4.0 \%$. To what temperature must it be raised?

In the circuit shown in Fig. we saw earlier both $12.0 \Omega$ batteries have insignificant internal resistance and the idealized ammeter reads $1.50 \mathrm{~A}$ in the direction shown. Find the emf $\mathcal{E}$ of the battery. Is the polarity shown correct?

In the circuit shown in the given figure, the batteries have negligible internal resistance and the meters are both idealized. With switch S open, the voltmeter reads 15.0 V. What will the ammeter read when the switch is closed?

(II) Estimate the number of moles of water in all the Earth's oceans. Assume water covers $75 \%$ of the Earth to an average depth of $3 \mathrm{~km}$.

One end of an insulated metal rod is maintained at 100 °C and the other end is maintained at 0.00 °C by an ice water mixture. The rod has a length of 50.0 cm and a cross-sectional area of 1.00 cm2. The heat conducted by the rod melts a mass of 9.50 g of ice in a time of 15.0 min. Find the thermal conductivity of the metal.

A brass plug is to be placed in a ring made of iron. At $15^{\circ} \mathrm{C}$, the diameter of the plug is $8.755 \mathrm{~cm}$ and that of the inside of the ring is $8.741 \mathrm{~cm}$. They must both be brought to what common temperature in order to fit?

(II) Wine bottles are never completely filled: a small volume of air is left in the glass bottle's cylindrically shaped neck (inner diameter $d=18.5 \mathrm{~mm}$ ) to allow for wine's fairly large coefficient of thermal expansion. The distance $H$ between the surface of the liquid contents and the bottom of the cork is called the "headspace height" (Fig. 17-22), and is typically $H=1.5 \mathrm{~cm}$ for a $750-\mathrm{mL}$ bottle filled at $20^{\circ} \mathrm{C}$. Due to its alcoholic content, wine's coefficient of volume expansion is about double that of water; in comparison, the thermal expansion of glass can be neglected. Estimate $H$ if the bottle is kept at $10^{\circ} \mathrm{C}.$

To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.871 cm in diameter is to be placed in a hole 1.869 cm in diameter at $20^{\circ} \mathrm{C}$. To what temperature must the rivet be cooled if it is to fit in the hole?

At t = 0 a grinding wheel has an angular velocity of 24.0 rad/s. It has a constant angular acceleration of $30.0 \text { rad} / \mathrm { s } ^ { 2 }$ until a circuit breaker trips at t = 2.00 s. From then on, it turns through 432 rad as it coasts to a stop at constant angular acceleration. Through what total angle did the wheel turn between t = 0 and the time it stopped?