(a) A woman climbing the Washington Monument metabolizes 6.00×102kJ of food energy. If her efficiency is 18.0%, how much heat transfer occurs to the environment to keep her temperature constant? (b) Discuss the amount of heat transfer found in (a). Is it consistent with the fact that you quickly warm up when exercising?

a. The total translational kinetic energy of the gas molecules is 1672 Joules.

b. The thermal energy of a gas molecule is equal to 1672 Joules.

c. The rms speed of the gas molecules is equal to 512.83 m/s.

Given the following data:

• Mass of hydrogen gas = 1.3 gram.

• Speed (rms), c = 1600 m/s.

• Work done = 500 Joules.

• Quantity of energy = 2000 Joules.

Scientific data:

• Mass of proton = kg.

• Avogadro constant =

a. To calculate the total translational kinetic energy of the gas molecules:

How to calculate translational kinetic energy.

First of all, we would determine the number of moles of hydrogen gas contained in 1.3 grams:

Note:Molar mass of hydrogen gas = 2 g/mol.

Number of moles = 0.65 moles.

Next, we would determine the number of molecules in 0.65 moles of hydrogen gas:

By stoichiometry:

1 mole = molecules.

0.65 mole = X molecules.

Cross-multiplying, we have:

X = = molecules.

Mathematically, total translational kinetic energy is given by this formula:

Substituting the given parameters into the formula, we have;

T = 1,671.68 ≈ 1672 Joules.

b. In Science, the total translational kinetic energy is equal to the thermal energy of a gas molecule.

Thermal energy = 1672 Joules.

c. To calculate the rms speed of the gas molecules:

Net energy = 172 Joules.

For the rms speed:

c = 512.83 m/s.

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Final answer:

The total translational kinetic energy and thermal energy of 1.3g of hydrogen gas with rms speed of 1600 m/s is 5.01x10^25 Joules. After work of 500 Joules is done to compress the gas and 2000 Joules of heat energy are transferred out, the kinetic and thermal energy remains the same, thus the rms speed remains largely the same (with a negligible change due to roundoff errors).

Explanation:

You're asking about the behavior of a hydrogen gas in terms of its kinetic and thermal energy, as well as changes in its root mean square (rms) speed as work is done to compress the gas and heat is transferred out of it.

Part A: The total translational kinetic energy can be calculated using the formula 1/2*m*v^2, where m is the mass and v is the speed. For hydrogen in monoatomic gas, 1.3g of hydrogen is about 0.65 moles. 1 mole's mass is about 1g, so 0.65 moles would be about 0.65g. Convert this to kilograms: 0.65g = 0.00065kg. To find the individual molecule's kinetic energy, you multiply by Avogadro's number (6.02*10^23) as there are that many molecules in a mole. Therefore, the Total translational kinetic energy = 1/2 * 0.00065 kg * (1600 m/s)^2 * 6.02x10^23 = 5.01x10^25 Joules.

Part B: At equilibrium, the thermal energy of a gas is equal to its kinetic energy, so the thermal energy would also be 5.01x10^25 Joules.

Part C: According to the principle of energy conservation, the final kinetic (and thus, thermal) energy of the gas will be its initial energy plus the work done on it minus the heat transferred out of it. Therefore, the final energy = 5.01x10^25 Joules + 500 Joules - 2000 Joules = 5.01x10^25 Joules. To find the new rms speed, you set this equal to the kinetic energy formula and solve for v. Doing so gets you a modulus change in the root mean square speed. Please note that this involves some simplifying assumptions and may not reflect what would happen in a more complex system.

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Answer:

361.46 N

Explanation:

= Coefficient of thermal expansion =

Y = Young's modulus for steel =

A = Area =

= Original length = 1.28 km

= Change in temperature =

Length contraction is given by

Also,

The tension in the wire is 361.46 N

Answer:

option (B)

Explanation:

Power, P = 600 W

mass of water, m = 250 g = 0.250 kg

T1 = 20° C

T2 = 80° C

ΔT = 80 - 20 = 60

specific heat of water, c = 4200 J/kg °C

Let the time taken is t.

Power x time = mass of water x specific heat of water x rise in temperature

600 x t = 0.250 x 4200 x 60

t = 105 second

option (B)

Final answer:

To heat 250g of water from 20°C to 80°C using a 600W microwave, it would approximately take 100 seconds.

Explanation:

In order to solve this problem, we first need to know the specific heat capacity of water, which is approximately 4.18 J/g°C. This value represents the amount of energy required to raise 1 gram of water by 1 degree Celsius. Given this value, we'll need to use the formula q = mcΔT, where q is the energy transferred (in joules), m is the mass of the water (in grams), c is the specific heat capacity (in J/g°C), and ΔT is the change in temperature (in °C).

We're given that the initial temperature of water is 20°C and we want to heat it to 80°C, so ΔT = 80°C - 20°C = 60°C. Substituting the known values into the formula, we get: q = 250g * 4.18 J/g°C * 60°C = 62700 J. Now, we know that power (P) = q/t. Given that the microwave oven operates at 600 W (or 600 J/s), we can solve for t: 62700 J ÷ 600 J/s ≈ 104.5 seconds. So, the closest answer would be (B) 100 seconds, considering the approximate value.

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Final answer:

The question involves computation of frequency, intensity, Poynting vector and electric field of an electromagnetic wave, and comparison between two such waves. The solutions result in approximately: 10 GHz for frequency, 3.07 x 10^-12 W/m^2 for intensity, 1.3 X 10^-19 W/m^2 for the z-component of Poynting vector, and 1.43 V/m for the electric field. Moreover, the comparison yields that SIIz is less than zero and not equal to Sz in magnitude.

Explanation:

The subject of your question relates to

electromagnetic waves

and their properties such as frequency, intensity, Poynting vector, and the electric field component. These concepts belong to the realm of physics, and more specifically, are topics in the study of electromagnetic theory.

To solve your questions:

1. The frequency f can be found using the formula: f = c/λ where c is the speed of light in vacuum (~3x10^8 m/s). For λ = 3 cm or 0.03 m, computation yields f ≈ 10^10 Hz or 10 GHz.
2. The intensity I of an electromagnetic wave in a vacuum can be given by the equation I = 0.5*c*ε0*E^2, where E is the electric field amplitude. To compute I, first, we need to find E which is given by E = c*B, where B is the magnetic field amplitude. Here, B is the square root of (Bx^2 + By^2) resulting in approximately 4.77*10^-6 T. Thus, E ≈ 1.43 V/m and solving for I gives us I ≈ 3.07 x 10^-12 W/m^2.
3. The z-component of the Poynting vector Sz at a specified point and time is given by Sz = E x H, where H = B/μ0, μ0 represents the permeability of free space. At t = 0, Sz = Ex*Hy - Ey*Hx = Ex*By, resulting in Sz ≈ 1.3 x 10^-19 W/m^2.
4. The x-component of the electric field at t = 0 Ex≈1.43 V/m.
5. Finally, comparing Sz of both waves (magnitudes and signs), we find that SIIz < 0 and the magnitude of SIIz does not equal the magnitude of Sz.

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Final answer:

The frequency of the wave is 10 GHz. While we can't expressly calculate the intesity, Sz, and Ex without more information, we can note that if the signs of Bx and By are swapped in a new wave, the Poynting vector would be flipped, hence SIIz would be negative and of equal magnitude to Sz.

Explanation:

An electromagnetic wave propagating through vacuum is described by certain electromagnetic fields which are associated with frequency, intensity, and Poynting vector which indicates the direction of energy flow. These can be calculated using certain formulas derived from wave equations.

Frequency can be acquired from the wavelength (λ) with the formula: f = c/λ, where c is the speed of light in vacuum. Using given λ = 3 cm, we get f = 10^10 Hz or 10 GHz.

The total Intensity (I) can be calculated as the average of the sum of the intensities in the x and y direction, given by: 1/2 ε_0 c E^2, where ε_0 is the permittivity of free-space and E is the electric field amplitude. However, more information might be needed to calculate this value. Similarly, without further information, we cannot calculate the exact values of Sz and Ex.

When comparing Sz and SIIz, if the signs of Bx and By are swapped in a new wave, this would flip the direction of the Poynting vector (since it is related to E × B), hence SIIz < 0 and its magnitude would still equal to Sz because the magnitudes of Bx and By do not change.

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To lift a 10-kg bundle of shingles with an upward acceleration of 1.5 m/s², a motor with a pulley of radius 0.17 m must provide a torque of at least 19 N.m.

We wish to use a motor to lift a 10-kg (m) bund of shingles with an upward acceleration of 1.5 m/s² (a).

The resulting force (F = m.a) is the difference between the tension (T) of the pulley and the weight (w = m.g) of the shingles.

where,

• g: gravity

Then, we can calculate the minimum torque (τ) that the motor must apply using the following expression.

where,

• r: radius of the pulley

To lift a 10-kg bundle of shingles with an upward acceleration of 1.5 m/s², a motor with a pulley of radius 0.17 m must provide a torque of at least 19 N.m.

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Answer:

Explanation:

It is given that,

Mass of bundle of shingles, m = 10 kg

Upward acceleration of the shingles,

The radius of the motor of the pulley, r = 0.17 m

Let T is the tension acting on the shingles when it is lifted up. It can be calculated as :

T = 113 N

Let is the minimum torque that the motor must be able to provide. It is given by :

So, the minimum value of torque is 19.21 N-m. Hence, this is the required solution.