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The rms speed of the molecules in 1.3 g of hydrogen gas is 1600 m/s.Part A. What is the total translational kinetic energy of the gas molecules?
Part B. What is the thermal energy of the gas?
Part C. 500J of work are done to compress the gas while, in the same process, 2000J of heat energy are transferred from the gas to the environment. Afterward, what is the rms speed of the molecules?

Answers

Answer 1

Answer:

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 = $1.67 * 10^(-27)$ kg.

Avogadro constant = $6.02 * 10^(23)$

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.

$Number \;of \;moles = \frac {mass}{molar\;mass}\n\nNumber \;of \;moles = \frac {1.3}{2}$

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 = $6.02 * 10^(23)$ molecules.

0.65 mole = X molecules.

Cross-multiplying, we have:

X = $0.65 * 6.02 * 10^(23)$ = $3.913 * 10^(23)$ molecules.

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

$T = (1)/(2) mc^2$

Substituting the given parameters into the formula, we have;

$T = (1)/(2) * 2 * 1.67 * 10^(-27) * 3.913 * 10^(23) * (1600)^2\n\nT = 6.53 * 10^(-4) * 2560000$

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:

$Net\;energy = 500 + 1672 -2000$

Net energy = 172 Joules.

For the rms speed:

$172 = (1)/(2) * 2 * 1.67 * 10^(-27) * 3.913 * 10^(23) * c^2\n\n172 = 6.54 * 10^(-4) c^2\n\nc = \sqrt{(172)/(6.54 * 10^(-4)) } \n\nc=√(262996.95)$

c = 512.83 m/s.

Read more on rms speed here: brainly.com/question/7427089

Answer 2

Answer:

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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Answers

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Explanation:

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La altura vertical máxima alcanzada es de 31,88 m.

Tenemos la siguiente información de la pregunta;

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Answers

Answer :

(a). The wavelength of electron is 26.22 μm.

(b).The wavelength of car is $2.38*10^(-38)\ m$

Explanation :

Given that,

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Answers

Answer:

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So,

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Also,

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Answers

Answer:

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Explanation:

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Let K be the spring constant.

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