In a production facility, 3-cm-thick large brass plates (k = 110 W/m·K, Ï = 8530 kg/m 3 , c p = 380 J/kg·K, and α = 33.9 à 10 -6 m 2 /s) that are initially at...

An average person generates heat at a rate of 84 W while resting. Assuming one-quarter of this heat is lost from the head and disregarding radiation, determine the average surface temperature of the...

A thermocouple, with a spherical junction diameter of 0.5 mm, is used for measuring the temperature of hot air flow in a circular duct. The convection heat transfer coefficient of the air flow can be...

A typical section of a building wall is shown in Fig. P17126. This section extends in and out of the page and is repeated in the vertical direction. The wall support members are made of steel (k = 50...

A 15 mm 15 mm silicon chip is mounted such that the edges are flush in a substrate. The chip dissipates 1.4 W of power uniformly, while air at 20C (1 atm) with a velocity of 25 m/s is used to cool...

A small aircraft has a wing area of 35 m 2 , a lift coefficient of 0.45 at takeoff settings, and a total mass of 4000 kg. Determine (a) The takeoff speed of this aircraft at sea level at standard...

A typical section of a building wall is shown in Fig. P1758. This section extends in and out of the page and is repeated in the vertical direction. The wall support members are made of steel (k = 50...

Consider a 4-m 4-m 4-m cubical furnace whose floor and ceiling are black and whose side surfaces are reradiating. The floor and the ceiling of the furnace are maintained at temperatures of 550 K...

Hot water at 90°C enters a 15-m section of a cast iron pipe (k = 52 W/mK) whose inner and outer diameters are 4 and 4.6 cm, respectively, at an average velocity of 1.2 m/s. The outer surface of...

The two concentric spheres of diameters D i = 20 cm and D o = 30 cm are separated by air at 1 atm pressure. The surface temperatures of the two spheres enclosing the air are T i = 320 K and T o = 280...

A 1.5-m-diameter, 4-m-long cylindrical propane tank is initially filled with liquid propane, whose density is 581 kg/m 3 . The tank is exposed to the ambient air at 25°C in calm weather. The...

Consider a 1.2-m-high and 2-m-wide glass window with a thickness of 6 mm, thermal conductivity k = 0.78 W/m·K, and emissivity ε = 0.9. The room and the walls that face the window...

A circular ceramic plate that can be modeled as a blackbody is being heated by an electrical heater. The plate is 30 cm in diameter and is situated in a surrounding ambient temperature of 15°C...

A single pass heat exchanger is to be designed to heat 100,000 lbm of water in an hour from 60F to 100F by condensation of water vapor at 230F on the shell side. Each tube has an inner diameter of...

Hot water enters a double-pipe counter-flow waterto-oil heat exchanger at 190F and leaves at 100F. Oil enters at 70F and leaves at 130F. Determine which fluid has the smaller heat capacity rate and...

Hot water (c ph = 4188 J/kgK) with mass flow rate of 2.5 kg/s at 100C enters a thin-walled concentric tube counter-flow heat exchanger with a surface area of 23 m 2 and an overall heat transfer...

Reconsider Prob. 2287. Using an appropriate software, investigate the effects of the inlet temperature of hot water and the heat transfer coefficient on the rate of heat transfer and the surface...

A cross-flow heat exchanger with both fluids unmixed has an overall heat transfer coefficient of 200 W/m 2 K, and a heat transfer surface area of 400 m 2 . The hot fluid has a heat capacity of 40,000...

Steam is to be condensed on the shell side of a 1-shell-pass and 8-tube-passes condenser, with 50 tubes in each pass, at 30°C (h fg = 2431 kJ/kg). Cooling water (c p = 4180 J/kg·K) enters...

A single-pass cross-flow heat exchanger uses hot air (mixed) to heat water (unmixed), flowing with a mass flow rate of 3 kg/s, from 30°C to 80°C. The hot air enters and exits the heat...

Which of the following reactions are allowed, and which are forbidden, by the conservation laws appropriate to weak interactions? (a) + p + + n, (b) e + p e + + + p, (c) + e + e , (d) ...

Assuming the BetheBloch formula is valid for low energies, show that the rate of ionisation has a maximum (the Bragg peak) and find the kinetic energy of protons in iron for which this maximum would...

Show that the scattering variable defined by (8.28) reduces to (8.30) in the rest frame of the proton. Hence show that the scaling variable (8.29) lies in the range 0 x 1 if the lepton masses are...

Would you expect the widths of three chi states listed in Table 6.14 to be bigger, smaller or about the same as the widths of the J/Ï(3097) and Ï(3686)? Check your answer with the...

Three particles, labelled 1, 2, 3, are produced in a given experiment at a fixed centre-of-mass energy. If show that the sum of the squared invariant masses is m,3 (, + E,)* - (. + ), ; 3 m,c+ m, ' +...

Show that the total decay rates for the reactions K 0 e + e and K 0 e e are equal if CP is conserved.

Draw the dominant lowest-order diagrams for the double Higgs boson production reaction e + e H 0 H 0 Z 0 at a total centre-of mass energy of 500 GeV.

By decomposing the Ï 0 Ï 0 state into components of definite isospin I, using the methods given in Appendix C, it can be shown that where the phase factors are due to the strong interaction...

Which of the following six decays are allowed in lowest-order weak interactions? (a) K + + + + + e + e , (b) K + + + e + e , (c) 0 + e + + e , (d) 0 + e + v e , (e) 0 p + + ...

How many watts of power do you expend when you exert a force of 6 N that moves a book 2 m in a time interval of 3 s?

Complete the calculation of the mass of Earth as outlined in Section 2.7.

A friend says that astronauts inside the International Space Station (ISS) are weightless because theyre beyond the pull of Earths gravity. Correct your friends reasoning.

Make a small hole near the bottom of an open tin can. Fill the can with water, which then proceeds to spurt from the hole. If you cover the top of the can firmly with the palm of your hand, the flow...

The electric field outside a charged conducting sphere is the same as if the charge were centered at its origin.Use this fact to calculate the capacitance of a sphere of radius R, taking the second...

A cloud-to-ground lightning bolt can be modeled as a parallel plate capacitor discharge, with Earths surface and the bottom of the cloud forming the two plates. A particular bolt of lightning passes...

Electrical power is often used to boil water for cooking.Here are the results of an experiment: a liter of water initially at 30 C was boiled on an electric stove top burner. The burner is rated at...

Consider the motor. If the resistance in the wire wrapping the rotor is 1, compute the energy lost under the conditions described. What fraction of energy is lost to Joule heating in this...

Consider a long, hollow solenoid of volume V.Show that, ignoring end effects, its inductance is L = n 2 V 0 , and that the magnetic energy it stores E EM = LI 2 /2 can be written in the form of eq....

Prove that the mutual inductance is a symmetric relation, M 12 = M 21 , by computing the energy stored when current I 1 is established in loop 1 and then current I 2 is established in loop 2. Then...

Derived the EMF on a wire loop rotating in a magnetic field using the Lorentz force law to compute the forces on the mobile charges. Although Faraday?s law of induction does not apply in a rotating...

Consider the transformer in Figure 3.25 . Suppose the load is a resistor R and that the transformer is ideal, with M 2 = L S L P and all magnetic flux lines passing through both inductors. Show that...

The strongest radio stations in the US broadcast at a power of 50 kW. Assuming that the power is broadcast uniformly over the hemisphere above Earths surface, compute the strength of the electric...

Derive the wave equation for B analogous to eq.? a2 E 1 aB V x at 1 V x (V x E) at2 HOEO 1 -vE.

Suppose an electromagnetic plane wave is absorbed on a surface oriented perpendicular to the direction of propagation of the wave. Show that the pressure exerted by the radiation on the surface is...

A string of length L is initially stretched into a zigzag profile, with linear segments of string connecting the (x, f(x)) points (0, 0), (L/4, a), (3L/4,a), (L, 0). Compute the Fourier series...

What is the pressure exerted by a beam of light on a perfect mirror from which it reflects at normal (perpendicular) incidence? Generalize this to light incident at an angle to the normal on an...

Consider a cylindrical resistor of cross-sectional area A and length L. Assume that the electric field E and current density j are uniform within the resistor. Prove that the integrated power...

A cylindrical tube oriented vertically on Earths surface, closed at the bottom and open at the top (height 100m, cross-sectional area 1m 2 ) initially contains air at a pressure of one atmosphere and...

1 Plancks constant is very small on the scale of human affairs. Compare the angular momentum of a childs marble spinning at 60 rpm with Plancks constant. Compare the energy of the same marble...

A particle of mass m in a potential V(x) has an energy basis state with wave function ? What is the potential and what is the energy of this state? What is the value of the constant C? Y(x) = C/...

The interatomic potential for diatomic molecules like O 2 and N 2 can be approximated near its minimum by a simple harmonic oscillator potential 1/2 kx 2 . Consider the classical motion of a diatomic...

Consider a macroscopic oscillator, given by a mass of m = 0.1 kg on a spring with spring constant k = 0.4N/m. What is the natural frequency of this oscillator? Considering this as a quantum system,...

A heat engine operates between a temperature T + and the ambient environment at temperature 298K. How large must T + be for the engine to have a possible efficiency of 90%? Can you find some...

In a typical step in the CPU of a computer, a 32-bit register is overwritten with the result of an operation. The original values of the 32 bits are lost. Since the laws of physics are reversible,...

The power output of air conditioners is measured intons, an ancient nomenclature dating back to the days when air was cooled by blowing it over blocks of ice.A ton of air conditioning is defined to...

The Morse potential parameters for oxygen are given by D e = 5.211 eV, = 2.78 1, and re =1.207 . Using the result from the previous problem, estimate the energy necessary to excite the oxygen...

Estimate the amount of CO 2 produced per kilogram of CaCO 3 in the calcination reaction (9.10). In addition to the CO 2 released in the reaction, include the CO 2 emitted if coal is burned (at 100%...

Another commonly used model for the potential energy of a diatomic molecule is the LennardJones(LJ) potential V(r) = ((r m /r) 12 2(r m /r) 6 ). Using the results of Problem 9.6, find the choice of...

Approximating the inter atomic potential as a harmonic oscillator with angular frequency vib , the vibrational - rotational energy levels of a diatomic molecule are given by E(n, J) = vib (n+1/2)+...

The convention we have used for LHV differs from the one offered by the US Department of Energy, which defines LHV as the amount of heat released by combusting a specified quantity (initially at 25 ...

Show that the method of refining tin explained in Example 9.3 will not work for alumina.

(Requires results from Problem 11.3) Consider the same engine as in Problem 11.3 but now run as an Atkinson cycle. The volume after expansion (V 4 ) is still 2 L, but the volume before compression (V...

Consider the Otto and Diesel cycles shown in Figure 11.13? The parameters have been chosen so both cycles have the same heat input and the same low temperature and pressure set point. Explain why the...

Modify the coal plant Rankine cycle described in 13.3.5 by including a regeneration cycle similar to the one shown in Figure 13.16(b) A fraction f of the steam is removed from the turbine and...

A rocket fuel should have high energy density (per kilogram) because the weight of the propellant is an important consideration. A favorite fuel is liquid hydrogen plus liquid oxygen. What is the...

In principle, and in the absence of electromagnetic or any other non-gravitational interactions, an electron and a proton should form a ?gravitational atom,? bound by the force of gravity. We know...

Potassium-40 ( 40 K) is a naturally occurring form of potassium whose -decays are responsible for some of Earths geothermal energy. 40 K can decay in two different ways. The probabilities per unit...

Einstein?s energy?momentum relation for a particle of mass m with momentum p is? Estimate the uncertainty in the x, y, and z components of the momentum of a quark confined in a (cubic) box of side...

Consider the ground state and the first and second excited states of a simple harmonic oscillator as described in 7. Verify the statement made in the text that the probability of finding the particle...

Verify the barrier penetration factor obtained for the parabolic barrier in Box 15.2.

Compute the exact amplitude for transmission and reflection of a particle from a rectangular potential barrier of height V 0? and width d by matching the wave function and its derivative at the...

Assume that thorium can be converted 100% into 233 U and used as a fission fuel. According to world thorium reserves are roughly 6 10 6 tonnes. How long could this amount of thorium supply 100% of...

Derive the relation quoted in eq. (17.7) ? between the binding energy of a neutral atom B(Z, A) and its mass excess ?(Z, A). B(Z, A) - n) + (| ) -(, A)

There is no stable nucleus with A = 5. This has profound consequences for the way stars burn and form elements. The two candidates for stable nuclei with A = 5 are 5 2 He and 5 3 Li. Look up or...

97% of naturally occurring calcium is calcium-40, 40 20 Ca. This may seem surprising, since if we use the semi-empirical mass formula to estimate the most stable nuclide with A = 40 we find Z 18....

Estimate the height of the Coulomb barrier between two protons as follows: the strong nuclear interaction potential between two protons at large separation is given by eq. (14.5) Add to this the...

Estimate a lower limit on the number of collisions a 1 MeV proton must make with atomic electrons before its energy is reduced to 10 eV. Why is it reasonable to ignore the atomic binding energy of...

The mass attenuation coefficients (/) for 1.5 MeV photons inconcrete ( = 2.35 g/cm 3 ) and lead (=11.4 g/cm 3 ) are both about 0.5 cm 2 /g. How thick must concrete or lead shielding be in order to...

In 20.3.1 it is stated that activity a is often used as measure of the mass of radio nuclide in a sample m. Show that for a radio nuclide with half-life t 1/2 and atomic mass A, this relationship ism...

A nuclear accident has exposed a 70 kg worker to 1 Ci of 2 MeV photons for about one minute. Assuming that all the energy of absorbed photons is deposited in the body, with uniform distribution,what...

Particle physics experiments are shielded from cosmic ray muons by placement underground, often in old mines. Cosmic ray muons have been detected at 2000 feet below ground at the Home stake Gold Mine...

40 K accounts for 0.0117% of naturally occurring potassium and potassium accounts for about 0.2% of the human body mass.Considering only the dominant decay of 40 K, which yields a -decay electron of...

Confirm by explicit computations the assertions made in Example 21.1 that the Hamiltonian is invariant under translation and rotation so that total momentum and angular momentum are conserved.

According to special relativity, the speed of light should be the same as seen by two observers moving at different relative velocities. In Newtonian physics, an observer (2) moving at a velocity v...

Compute or estimate the fraction of radiated thermal energy that is in the visible range (wavelength 400750 nm) for the following two radiation spectra: (a) solar radiation, assumed to be perfect...

Consider two events seen by observer (1), who chooses her coordinates so that the first event occurs at the space-time origin x ? 1 = (0, 0, 0, 0), while the second event occurs at x? ? 1 = ( c? t 1...

Compute the frequency max corresponding to the maximum power of radiation for a blackbody at temperature T = 280 K. This is roughly the average temperature of Earths surface. Compute the wavelength...

The average radius of Mars orbit is 2.28 10 8 km. Compute the solar constant for Mars.

Suppose that the surface temperature of the Sun were to increase by 3% from the current value, assuming for simplicity that the radius of the Sun stays fixed. By how much would the solar constant on...

Suppose the wind speed obeys a Gaussian frequency distribution in the two components of the horizontal velocity v = (v 1 , v 2 ), Show that the wind speed distribution, f (v) = dP/dv, Where? is a...

Assume that the pressure in a volume of air can be expressed to first order in a local coordinate system (x, y, z) as p = p 0 + f x + O(x 2 , y 2 , xy, . . .). Show from the balance of forces on a...

Assume that a region of continental crust has a typical surface heat flux of 65 mW/m 2 , crustal density of 2750 kg/m 3 , and typical crustal abundances of radioactive nuclides (as given in Table...

Figure 12.34 shows the trajectory of a comet passing near the Sun. Describe how Newton would explain the deviation in the comets path from a straight line. Repeat the explanation as it might be given...

How are frequency and period related to each other?

Bar magnets are moved into the wire coils in identical quick fashion. Voltage induced in each coil causes a current, as indicated on the galvanometer. Neglect the electrical resistance in the loops...

It is estimated that six large pizzas are about right to serve a physics club meeting of 30 students. How many pizzas would be required if the group grows to 50 students?

If a mile is 5280 ft long and a yard contains 3 ft, how many yards are there in a mile?

A common speed limit in Vancouver, British Columbia, is 80 km/hr. If you are going 55 MPH, are you speeding? Show by converting 55 MPH to km/hr using the conversion factors on the inside front cover.

In the United States a common quantity of hard liquor was historically a fifth, which represents a fifth of a US gallon. However, since the US wants to market its alcohol globally, and everyone else...

Starting from rest, a car accelerates at a constant rate of 3.0 m/s 2 for a time of 5 seconds. a. Compute the velocity of the car at 1 s, 2 s, 3 s, 4 s, and 5 s and plot these velocity values against...