Q: A small piece of copper (mass $$m = 0.10 kg) is $$heated to $$200^{\circ}$$\mathrm{C}$$ and placed in a well-insulated cylinder containing monatomic helium gas at 25$$^{\circ}$$\mathrm{C}$$ and $$1.0$$ atm. The cylinder has radius $$r = 0.12 m $$and length $$L = 1.30 m. $$What is the number of moles of helium gas in the cylinder? (Use $$V = \pi r^2$ L$$ and $$PV = nRT$$ with $$R = 8.314 J/($$mol·K))

$$n = \dfrac{1.013 \times 10^5$ \times \pi \times (0.12)^2$ \times 1.30}{8.314 \times (273.15 + 25)}$$

Question 1

Refer to the equipotential diagram provided. At point P, what is the direction of the electric field?

Accepted Answer

Down

Question 2

A small piece of copper (mass $$m = 0.10 kg) is $$heated to $$200^{\circ}$$\mathrm{C}$$ and placed in a well-insulated cylinder containing monatomic helium gas at 25$$^{\circ}$$\mathrm{C}$$ and $$1.0$$ atm. The cylinder has radius $$r = 0.12 m $$and length $$L = 1.30 m. $$What is the number of moles of helium gas in the cylinder? (Use $$V = \pi r^2$ L$$ and $$PV = nRT$$ with $$R = 8.314 J/($$mol·K))

Accepted Answer

$$n = \dfrac{1.013 	imes 10^5$ 	imes \pi 	imes (0.12)^2$ 	imes 1.30}{8.314 	imes (273.15 + 25)}$$

Question 3

A block of aluminum expands linearly by $$0.001$$ for a temperature increase $$\Delta T. If $$the temperature increases by $$2\Delta T$$, what is the approximate fractional increase in the block’s volume?

Accepted Answer

$$0.003$$

Question 4

A $$1$$ gram piece of ice at $$0^{\circ}$$\mathrm{C}$$ absorbs 300$ J of heat. Given the latent heat of fusion for water is 3.34$$ 	imes $$10^5 J/kg $$and the specific heat of water is $$4186 J/(kg$$·$$^{\circ}C$$), what is the final temperature of the system?

Accepted Answer

$$0^{\circ}$$\mathrm{C}$$

Question 5

An ideal gas expands adiabatically, doing $$3000 J of $$work. What is the change in the internal energy of the gas during this process?

Accepted Answer

$$-3000 J$$

Question 6

A cylindrical nichrome wire carries a current of $$4.0 A $$when connected to a battery. Another wire, half as long and twice the radius, is connected to the same battery. What is the current through this wire?

Accepted Answer

$$16.0 A$$

Question 7

A device with resistance $$R = 240\ \Omega is $$attached to an AC outlet with $$V_{\mathrm{rms}} = 120 V. $$What is the maximum current through the device?

Accepted Answer

$$0.71 A$$

Question 8

A section of wire carrying $$1.0 A is $$bent into an L-shape with $$4 m in $$the $$+x$$ direction and $$3 m in $$the $$+y$$ direction, placed in a $$1.0 T $$field in the $$-y$$ direction. What is the magnitude and direction of the magnetic force on the wire?

Accepted Answer

$$7 N $$into page

Question 9

A positive point charge moves to the right at the center of a loop of wire carrying a counterclockwise current. What is the direction of the magnetic force due to the current loop on the moving charge?

Accepted Answer

Out of the page

Question 10

The primary and secondary sides of a conventional 'step up' transformer share the same:

Accepted Answer

Magnetic flux through each loop

Question 11

A heat engine absorbs $$Q_{in,tot}$$ from a hot reservoir and expels $$Q_{out,tot} to a $$cold reservoir. What is the efficiency $$e of $$the engine?

Accepted Answer

$$e = 1 - \dfrac{Q_{out,tot}}{Q_{in,tot}}$$

Question 12

A parallel-plate capacitor is filled with a dielectric of constant $$\kappa. $$What happens to the capacitance?

Accepted Answer

$$C' = \kappa C_0$

Understanding Electric Field Direction from Equipotential Curves

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