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ycow [4]
2 years ago
13

Five-gram samples of copper and aluminum are at room temperature. Both receive equal amounts of energy due to heat flow. The spe

cific heat capacity of copper is 0.09 cal/g°C, and the specific heat capacity of aluminum is 0.22 cal/g°C. Which of the following statements is true?
a. The temperature of each sample increases by the same amount.
b. The aluminum will get hotter than the copper.
c. The copper will get hotter than the aluminum.
d. The temperature of each sample decreases by the same amount
Physics
1 answer:
hammer [34]2 years ago
5 0

Answer:

  • <u><em>c. The copper will get hotter than the aluminum.</em></u>

Explanation:

The <em>energy due to heat flow</em>, i.e. the heat energy, is proportional to the product of the mass, the <em>specific heat capacity</em>, and the change in <em>temperature</em>:

          Heat=mass\times \text{specific heat capacity }\times\Delta T

From which you obtain:

     \Delta T=\dfrac{Heat}{mass\times \text{specific heat capacity}}

That equation tells that the change in temperature is inversely related to the product of the mass and the specific heat.

In the problem, the masses of the samples of copper and aluminum are equal (<em>5.00g</em>) and both samples receive <em>equal amounts of energy due to heat flow</em>, thus the only difference is the <em>specific heat capacity</em> of each sample.

From the above stated relationship between the change in temperature, the heat, the mass, and the specific heat capacity, under the assumption of all the other conditions equal (heat energy and mass), the higher the specific heat capacity the lower the change in temperature, and the lower the specific heat capacity the greater the change in temperature.

The heat capacity of copper (0.09 cal/g°C) is lower than the specific heat capacity of aluminum is (0.22 cal/g°C), thus the increase in temeperature of the copper sample will be greater than that of the aluminum sample. This means that <em>the copper will get hotter than the aluminum (option c.)</em>

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Assuming Earth's gravity, the formula for the flight of the particle is: 

<span>s(t) = -16t^2 + vt + s = -16t^2 + 144t + 160. </span>

<span>This has a maximum when t = -b/(2a) = -144/[2(-16)] = -144/(-32) = 9/2. </span>

<span>Therefore, the maximum height is s(9/2) = -16(9/2)^2 + 144(9/2) + 160 = 484 feet. </span>
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Explanation:

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A sample of monatomic ideal gas occupies 5.00 L at atmospheric pressure and 300 K (point A). It is warmed at constant volume to
leonid [27]

Answer:

(a) 0.203 moles

(b) 900 K

(c) 900 K

(d) 15 L

(e) A → B, W = 0, Q = Eint = 1,518.91596 J

B → C, W = Q ≈ 1668.69974 J Eint = 0 J

C → A, Q = -2,531.5266 J, W = -1,013.25 J, Eint = -1,518.91596 J

(g) ∑Q = 656.089 J, ∑W =  655.449 J, ∑Eint = 0 J

Explanation:

At point A

The volume of the gas, V₁ = 5.00 L

The pressure of the gas, P₁ = 1 atm

The temperature of the gas, T₁ = 300 K

At point B

The volume of the gas, V₂ = V₁ = 5.00 L

The pressure of the gas, P₂ = 3.00 atm

The temperature of the gas, T₂ = Not given

At point C

The volume of the gas, V₃ = Not given

The pressure of the gas, P₃ = 1 atm

The temperature of the gas, T₂ = T₃ = 300 K

(a) The ideal gas equation is given as follows;

P·V = n·R·T

Where;

P = The pressure of the gas

V = The volume of the gas

n = The number of moles present

R = The universal gas constant = 0.08205 L·atm·mol⁻¹·K⁻¹

n = PV/(R·T)

∴ The number of moles, n = 1 × 5/(0.08205 × 300) ≈ 0.203 moles

The number of moles in the sample, n ≈ 0.203 moles

(b) The process from points A to B is a constant volume process, therefore, we have, by Gay-Lussac's law;

P₁/T₁ = P₂/T₂

∴ T₂ = P₂·T₁/P₁

From which we get;

T₂ = 3.0 atm. × 300 K/(1.00 atm.) = 900 K

The temperature at point B, T₂ = 900 K

(c) The process from points B to C is a constant temperature process, therefore, T₃ = T₂ = 900 K

(d) For a constant temperature process, according to Boyle's law, we have;

P₂·V₂ = P₃·V₃

V₃ = P₂·V₂/P₃

∴ V₃ = 3.00 atm. × 5.00 L/(1.00 atm.) = 15 L

The volume at point C, V₃ = 15 L

(e) The process A → B, which is a constant volume process, can be carried out in a vessel with a fixed volume

The process B → C, which is a constant temperature process, can be carried out in an insulated adjustable vessel

The process C → A, which is a constant pressure process, can be carried out in an adjustable vessel with a fixed amount of force applied to the piston

(f) For A → B, W = 0,

Q = Eint = n·cv·(T₂ - T₁)

Cv for monoatomic gas = 3/2·R

∴ Q = 0.203 moles × 3/2×0.08205 L·atm·mol⁻¹·K⁻¹×(900 K - 300 K) = 1,518.91596 J

Q = Eint = 1,518.91596 J

For B → C, we have a constant temperature process

Q = n·R·T₂·㏑(V₃/V₂)

∴ Q = 0.203 moles × 0.08205 L·atm/(mol·K) × 900 K × ln(15 L/5.00 L) ≈ 1668.69974 J

Eint = 0

Q = W ≈ 1668.69974 J

For C → A, we have a constant pressure process

Q = n·Cp·(T₁ - T₃)

∴ Q = 0.203 moles × (5/2) × 0.08205 L·atm/(mol·K) × (300 K - 900 K) = -2,531.5266 J

Q = -2,531.5266 J

W = P·(V₂ - V₁)

∴ W = 1.00 atm × (5.00 L - 15.00 L) = -1,013.25 J

W = -1,013.25 J

Eint = n·Cv·(T₁ - T₃)

Eint = 0.203 moles × (3/2) × 0.08205 L·atm/(mol·K) × (300 K - 900 K) = -1,518.91596 J

Eint = -1,518.91596 J

(g) ∑Q = 1,518.91596 J + 1668.69974 J - 2,531.5266 J = 656.089 J

∑W = 0 + 1668.69974 J -1,013.25 J = 655.449 J

∑Eint = 1,518.91596 J + 0 -1,518.91596 J = 0 J

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Artemon [7]

Answer:

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I am Lyosha [343]

Answer:

9 meters

Explanation:

Given:

Mass of Avi is, m=40\ kg

Spring constant is, k=176,400\ N/m

Compression in the spring is, x=20\ cm=0.20\ m

Let the maximum height reached be 'h' m.

Now, as the spring is compressed, there is elastic potential energy stored in the spring. This elastic potential energy is transferred to Avi in the form of gravitational potential energy.

So, by law of conservation of energy, decrease in elastic potential energy is equal to increase in gravitational potential energy.

Decrease in elastic potential energy is given as:

EPE=\frac{1}{2}kx^2\\EPE=\frac{1}{2}\times 176400\times (0.20)^2\\EPE=88200\times 0.04=3528\ J

Now, increase in gravitational potential energy is given as:

GPE=mgh=40\times 9.8\times h=392h

Now, increase in gravitational potential energy is equal decrease in elastic potential energy. Therefore,

392h=3528\\\\h=\frac{3528}{392}\\\\h=9\ m

Therefore, Avi will reach a maximum height of 9 meters.

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3 years ago
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