Problems with video solutions

CH18-01

An aluminum-alloy rod has a length of 12.920 cm at 12.00°C and a length of 12.962 cm at the boiling point of water. (a, 1 point) What is the length of the rod at the freezing point of water? (b, 1 point) What is the temperature if the length of the rod is 12.939 cm?

CH18-02

A small electric immersion heater is used to heat 78 g of water for a cup of instant coffee. The heater is labeled “120 watts” (it converts electrical energy to thermal energy at this rate). Calculate the time required to bring all this water from 19°C to 100°C, ignoring any heat losses. (The specific heat of water is 4186 J/kg·K.)

CH18-03

Calculate the minimum amount of energy in kilojoules required to completely melt 243 g of silver initially at 21.0oC. The melting point of silver is 962oC, its specific heat capacity is 0.236 kJ/kg·K and its latent heat of fusion is 105 kJ/kg.

CH18-04

The specific heat of a substance varies with temperature according to c = 0.71 + 0.39T + 0.083T², with T in °C and c in cal/g·K. Find the energy required to raise the temperature of 5.4 g of this substance from 8.0°C to 27°C.

CH18-05

A sample of gas expands from 1.0 m³ to 4.0 m³ while its pressure decreases from 40 Pa to 10 Pa. How much work is done by the gas if its pressure changes with volume via (a) path A, (b) path B, and (c) path C in the figure ?

CH18-06

The coefficient of volume expansion for glycerin is 49 10-5 C-1. Find the fractional change of its density at 30 °C

CH18-07

A copper block of mass 2.5 Kg is heated in a furnace to ΔT=500°C and then placed on a large ice block. Find the maximum amount of ice that will melt. Specific heat for Cu=0.39 J g -1 C-1, fusion for water 335 J g-1

CH18-08

A pendulum of mass m is hanging from a metallic wire of negligible mass, thermal expansion coefficient a and a period of 2 s at T=0°C. Find an expression so that its period can be calculated at any temperature!

CH18-09

How much would it cost to completely evaporate 0.5 Kg of water in a 400 W water boiler, from 20°C, if the 1 kW·h in Alabama costs 7.4 cents

CH19-01

A quantity of ideal gas at 11°C and 65 kPa occupies a volume of 8.6 m³. (a, 1point ) How many moles of the gas are present? (b, 1point) If the pressure is now raised to 230 kPa and the temperature is raised to 35.0°C, how much volume does the gas occupy? Assume no leaks.

CH19-02

The speed distribution for particles of a certain gas: P=C·v² for 0<v<v₀ and P=0 for v>v₀. Find an expression for the rms speed in terms of v₀.

Hint: the distribution function (i.e. integral) of all speeds must equal to 1 (normalization). The rms is the square of the integration v²·P(v)

CH19-03

Suppose 4.00 mol of an ideal diatomic gas, with molecular rotation but not oscillation, experienced a temperature increase of 60.0 K under constant-pressure conditions. Find the work W done by the gas

CH19-04

An ideal gas undergoes an adiabatic compression from p = 1.00 atm, V = 1.00 × 10⁶ L, T = 0.00°C to p = 1.00 × 10⁵ atm, V = 1.00 × 10³ L. (a) Is the gas monatomic, diatomic, or polyatomic? (b) What is its final temperature? (c) How many moles of gas are present? What is the total translational kinetic energy per mole (d) before and (e) after the compression? (f) What is the ratio of the squares of the rms speeds before and after the compression?

CH19-05

A quantity of 4.00 moles of a monatomic ideal gas goes from A to B as the figure shows expands from an initial volume of 0.100 m3 to a final volume of 0.300 m3 and pressure of 2.5 105 Pa (Fig. 12.7a). Compute (a) the work done on the gas, (b) the change in internal energy of the gas, and (c) the thermal energy transferred to the gas. Note that work is done ON the gas (W must be negative)

CH19-06

One mole of monoatomic gas is taken through a cycle, where A>B is adiabatic expansion, B>C is cooling at constant volume, C>D is adiabatic compression and D>A is heating at constant volume. If Ta=1000 K, Pb=2/3 Pa and Pc=1/3Pa. Find Td.

CH19-07

A container with an ideal gas also has a piston of mass M attached to a spring of uncompressed length L. We give the piston a slight push downwards, and assuming that the process is isothermal, find the period of oscillation of the piston

CH19-08

Temperature of an ideal gas initially at 27°C is raised by 6°C. Find the relative mean square velocity of the gas molecule

CH22-01

Two particles are fixed on an x axis. Particle 1 of charge 64.2 μC is located at x = -8.23 cm; particle 2 of charge Q is located at x = 23.6 cm. Particle 3 of charge magnitude 45.1 μC is released from rest on the y axis at y = 8.23 cm. What is the value of Q if the initial acceleration of particle 3 is in the positive direction of (a) the x axis and (b) the y axis?

CH22-02

A certain electric dipole is placed in a uniform electric field of magnitude 55 N/C. The figure gives the magnitude τ of the torque on the dipole versus the angle θ between field and the dipole moment P. The vertical axis scale is set by τ_s = 132 × 10^-28 N·m. What is the magnitude of p. Provide your answer accounting only for the decimal part x 10^-28 C·m

CH22-03

The figure shows three circular arcs centered at the origin of a coordinate system. On each arc, the uniformly distributed charge is given in terms of Q = 2.12 µC. The radii are given in terms of R = 8.27 cm. What are the (a) magnitude and (b) direction (relative to the positive x direction) of the net electric field at the origin due to the arcs?

CH22-04

Charge is uniformly distributed around a ring of radius R = 9.80 cm, and the resulting electric field magnitude E is measured along the ring's central axis (perpendicular to the plane of the ring). At what distance from the ring's center is E maximum? Note that the electric field at distance z passing through the center of the ring in the vertical is

CH22-05

Beams of high-speed protons can be produced in "guns" using electric fields to accelerate the protons. (a) What acceleration would a proton experience if the gun's electric field were 1.88 × 10⁴ N/C? (b) What speed would the proton attain if the field accelerated the proton through a distance of 1.44 cm?

CH22-06

An oil drop of radius r =1.64×10⁻⁶ m and mass density ρ_oil = 8.51×10² kg m³ is allowed to fall from rest and then enters into a region of constant external field E applied in the downward direction. The oil drop has an unknown electric charge q. The magnitude of the electric field is adjusted until the drop is suspended. Suppose this balancing occurs when E_j=−(1.92×10⁵ N/C)j. Find the ratio between the charge of the oil drop and the electron charge (1.6 10^-9 C)

CH22-07

A thin insulating rod of length L lies on the +x axis, with one end at +L/2, as shown. It has a non-uniform linear charge density λ that varies with position x according to λ = λ₀ x²/L² cos(πx/L) where λ₀ is a positive constant. What is the magnitude of the electric field at the origin?

CH22-08

Two identical charged spheres are suspended from a common point by two massless strings of lengths l. Initially the rest at distance d (i.e. at an angle) because of their mutual repulsion. Consider that d<< l. The charges begin to leak from both at a constant rate, and as a result the spheres begin to approach one another at a speed v. How does speed varies with their distance?

CH23-01

An electron is released 9.0 cm from a very long non-conducting rod with a uniform 6.8 μC/m. What is the magnitude of the electron's initial acceleration?

CH23-02

A hollow cylinder has a charge q. If φ is the electric flux in units V·m associated with the curved surface B then the electric flux in units V·m associated with the curved surface A is

CH23-03

A non uniform electric field is given by the expression E=(2y)i+(3z)j+(4x)z (N/C). Determine the electric flux through a rectangular xy surface extending from x=0 to x=3 meters and y=0 to y=2 meters

CH23-04

A charge distribution that is spherically symmetric but not uniform radially produces an electric field of magnitude E=a·r⁴, directed radially outward from the center of the sphere. Here r is the radial distance from that center, and a is a constant. What is the volume density of the charge distribution?

CH23-05

A sphere of radius A has a uniform volume charge f. The magnitude of the electric field at distance d>A from the center of the sphere is

CH23-06

The figure below shows, in cross section, two solid spheres with uniformly distributed charge throughout their volumes. Each has radius R. Point P lies on a line connecting the centers of the spheres, at radial distance R/2 from the center of sphere 1. If the net electric field at point P is zero, what is the ratio of q2/q1 the total charges?

CH23-07

A solid conducting sphere of radius 2.00 cm has a charge of 8.00 μC. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a charge of -4.00 μC. Find the electric field at (a) r 1.00 cm, (b) r 3.00 cm, (c) r 4.50cm, and (d) r 7.00cm from the center of this charge configuration.

CH23-08

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CH24-01

Five equal charges of 10 nC are located at x=2,4,5,10 and 20 m. If ε₀=10^-9/(36π), find the potential at the origin (x=0)

CH24-02

What is the magnitude of the electric field at point (3.00 i -2.00j+4.00k) if the electric potential in the region is given by V=2.00 xyz² (x,y,z in meters and V is in volts)

CH24-03

A particle with charge q is fixed at point P and a second particle of mass m and charge q is held at distance r1 from P. The second particle is released. Determine its speed when it is at distance r2 from P. Let q=3.1 micro C, m=20 mg, r1=0.90 mm and r2= 2.5 mm

CH24-04

An electric field is given by 4x a_x+ 2 a_y (V/m). Determine the work required to move a unit charge along a curve xy=4 from point (2,2) to (4,1)

CH24-05

A long solid conducting cylinder of radius 2 cm has an electric field at the surface of 160 N/C directed radially outward. Let points B and C be located 2 cm and 5 cm respectively from the central axis of the cylinder. Find V_B-V_C

CH24-06

Two isolated conducting spheres are separated by a large distance. Sphere 1 has a radius of R and an initial charge 3Q while sphere 2 has a radius of 3R and an initial charge 7Q. A very thin copper wire is now connected to the spheres to allow charge to flow between the spheres. How much charge will be transferred from sphere 2 to sphere 1? (Note that the charge transferred can be positive, negative or zero.)

CH24-07

The figure shows an electron moving along an electric dipole axis toward its negative side (x-axis). The electron was initially very far from the dipole with kinetic energy 100 eV (y-axis) as shown in figure). The horizontal scale is set by r_s=0.1 m. Find the dipole moment

CH24-08

A spherical shell with inner radius a=1 mm and outer radius b=2 mm is uniformly charged with a volume charge density ρ = 10^-2 C/m³. Find the potential at z= 1m. Your answer in X.XX Volts. Determine also the potential in the distance z > b.

CH25-01

A spherical shell with inner radius a=1 mm and outer radius b=2 mm is uniformly charged with a volume charge density ρ = 10^-2 C/m³. Find the potential at z= 1m. Your answer in X.XX Volts. Determine also the potential in the distance z > b.

CH25-02

The plate separation in a parallel plate capacitor is d and area A. It is charged to V volts and then the battery is disconnected. What is the work required to double the distance between the plates?

CH25-03

A capacitor is charged until 4.00 Joules of energy are stored. Then it is connected in parallel to a second capacitor. If the charge is is equally distributed what is the total energy stored in the system?

CH25-04

The capacitors in the figure are initially uncharged, with C1=4 micro F, C2=8 micro F and C3=12 micro F and battery is 12 V. When switch S is closed how many electrons travel through point a?

CH25-05

A parallel plate capacitor is filled each half with two dielectrics k1 and k2 as shown in the picture. The capacitor’s plate area is A and the distance is d. The capacitance of the system is

CH25-06

The plates S and T are charged with σ C/m2. The system of capacitor spring and object m is at mechanical and electrical static equilibrium, i.e. no mechanical parts nor charges are moving. Capacitor’s plates have area A=0.5 m and distance d=.01 m. The spring has constant k=100 N/m and the object is of mass m=10 Kg. Find the charge on one plate of the capacitor

CH25-07

Find the energy stored in the capacitor network shown in the figure given that this contraption is connected to a 7 V battery. Each capacitor is 2 micro F. Your answer in XX Joules

CH26-01

A silver wire has temperature coefficient of resistivity 4 10-3 °C-1 and its resistance at 20°C is 10 Ohm. Neglecting and dimension changes due to temperature, what is the resistance at 40°C?

CH26-02

Consider a hollow cylinder of length L =2 m and inner radius (1 mm) a and outer radius (2 mm). The material has resistivity ρ (100 Ohm m). Find the voltage applied between the two radii if the radial current flowing is 0.01 A.

(a)Suppose a potential difference is applied between the ends of the cylinder and produces a current flowing parallel to the axis. What is the resistance measured?

(b) If instead the potential difference is applied between the inner and outer surfaces so that current flows radially outward, what is the resistance measured?

CH26-03

Seawater has resistivity 25 Ohms · cm and an ion concentration of ~6·10²⁰ per cubic centimeter. What is their drift velocity inside a 2 meter long tube that is connected to a 12 V battery? Answer in cm s-1

CH26-04

A wire that has two sections with radii D1=4 R and D2=2 R is connected by a tapered section as the figure shows. Assume the current is uniformly distributed. The potential across a length of 2m is 10 μV. The number of charge carriers per cubic meter is 8.49 10²⁸. What is their drift speed?

CH26-05

If a piece of wire is stretched by n times what happens to the resistance?

CH26-06

A cylindrical resistor of radius 5.0 mm and length 2.0 cm is made of material with resistivity 3.5 10^-5 Ohm m. What is the electric field inside the resistor when the energy dissipation rate in the resistor is 1.0 W?

CH26-07

A standard 60 W 120 V light bulb has a tungsten filament that is 53.3 cm long and 46 μm in diameter. How does the resistivity calculated above compare to the value quoted in standard reference tables? (Divide what you get from solving this problem with the number for tungsten resistivity in this table (click: http://physicsa.com/reference.pdf)

CH26-08

A resistance coil R (=150 Ohms) is submersed in a calorimeter (i.e. an insulated tank with a liquid a thermometer). When no current runs through the resistor, the liquid, which has a specific heat capacity K=10³ (J/°C) looses temperature at a rate of Δθ=0.5 (°C/sec). Find current i as a function on R, K and A

CH27-01

Find current through the circuit

CH27-02

In the circuit below the current has reached a steady-state (does not change with time). Find the charge on the capacitor

CH27-03

A wire of resistance 10 Ohm is bent to form a circle. The PQ arc is one quadrant connected to a 3V battery with 1 Ohm resistance. Find the current over PQ

CH27-04

In the circuit below if the 5 Ohm resistance develops a heat of 42 J s-1, the heat in the 2 Ohm must be

CH27-05

Find the potential across the 1 micro F capacitor. Your answer in x.X Volts

CH27-06

All resistances in the circuit below are 1000 Ohms. If the current in the extreme right is 1 mA, find V_AB

CH27-07

Find the value of X so that the thermal power dissipated in resistance X is independent of its value. Given is R=9 Ohm and E=100 V. Your answer in X.X Ohms. Hint: express the power dissipated through X as a function of E, X and R. Do not substitute with numbers, but keep an algebraic expression Then think what “independent” of “X” means (maybe derivative?)

CH27-08

Derive an expression of voltage for a charging capacitor as a function of time t, resistance R, capacitance C connected to a battery of voltage E, if the capacitor had initial voltage V₀

Hint: Start with what you already know, that is the equation for voltage for a charging capacitor. How would this change if the capacitor had initial voltage V₀?

CH27-09

The capacitor in the figure is fully charged with q=10 μC. The battery is then removed and points A and C are shorted (brought together). Find the time that it takes until the charge becomes 4 μC.

Hint: re-sketch the circuit with A and C shortened (capacitor fully charged means steady state...)