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kobusy [5.1K]
3 years ago
7

To start a great night of doing physics homework, you sit down to pour yourself a good cup of coffee. Your coffee mug has a mass

137 g and a specific heat of 1089 J/kg K. The mug starts out at room temperature (23.8 o C). Your coffee has an initial temperature of 79.8 oC and has the same specific heat as water (4186 J/kg K).
1) Let's say you pour enough coffee into the mug so that the mass of coffee is equal to the mass of the mug. If we assume that no heat is lost to the outside room, once the mug and coffee reach the same temperature, will that temperature be closer to the initial temperature of the coffee or the initial temperature of the mug? (Notice that the mass of the coffee and the mass of the mug are the same.)
2) What is the final temperature of coffee and mug once they come to thermal equilibrium?
Tfinal = ____________ degrees c
3) Now lets assume that instead of the 137 g of coffee, you pour in 225 g of coffee. What is the final temperature of the coffee and mug? (Again, assume that you loose no heat to the outside.)
Tfinal = ____________ degrees c
4) Now lets say that along with the 225 g of coffee, you pour in 11.7 g of cream in your mug. The cream has an initial temperature of 5.2 oC and also has the same specific heat as water. What is the final temperature of the coffee, cream and mug? (Again, assume that you loose no heat to the outside.)
Tfinal = _____________ degrees c
Physics
1 answer:
astra-53 [7]3 years ago
6 0

Answer:

1) The temperature will be closer to water

2) T = 68.239°C

3) T = 72.142°C

4) T = 69.266 °C

Explanation:

1)

The temperature will be closer to water because  the heat capacity of water > heat capacity of coffee.

2)

137(1.089)(T - 23.8) = 137(4.186)(79.8 - T)

⇒(1.089)(T - 23.8) = (4.186)(79.8 - T)

⇒1.089 T - 25.9182 = 334.0428 - 4.186 T

⇒1.089 T +  4.186 T = 334.0428 + 25.9182

⇒5.275 T = 359.961

⇒ T = 68.239°C

3)

137(1.089)(T - 23.8) = 225(4.186)(79.8 - T)

⇒(149.193)(T - 23.8) = (941.85)(79.8 - T)

⇒149.193 T - 3550.7934 = 75159.63 - 941.85 T

⇒149.193 T +  941.85 T = 75159.63  + 3550.7934

⇒1091.043 T = 78710.4234

⇒ T = 72.142°C

4)

137(1.089)(T - 23.8) + 11.7(4.186)(T - 5.2)= 225(4.186)(79.8 - T)

⇒(149.193)(T - 23.8) + 48.9762(T - 5.2) = (941.85)(79.8 - T)

⇒149.193 T - 3550.7934  + 48.9762 T - 254.67624= 75159.63 - 941.85 T

⇒149.193 T +  941.85 T + 48.9762 T = 75159.63  + 3550.7934 + 254.67624

⇒1091.043 T + 48.9762 T = 78710.4234 + 254.67624

⇒1140.0192 T = 78965.09964

⇒ T = 69.266 °C

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An electron moving to the left at 0.8c collides with a photon moving to the right. After the collision, the electron is moving t
SVETLANKA909090 [29]

Answer:

Wavelength = 2.91 x 10⁻¹² m, Energy = 6.8 x 10⁻¹⁴

Explanation:

In order to show that a free electron can’t completely absorb a photon, the equation for relativistic energy and momentum will be needed, along the equation for the energy and momentum of a photon. The conservation of energy and momentum will also be used.

E = y(u) mc²

Here c is the speed of light in vacuum and y(u) is the Lorentz factor

y(u) = 1/√[1-(u/c)²], where u is the velocity of the particle

The relativistic momentum p of an object of mass m and velocity u is given by

p = y(u)mu

Here y(u) being the Lorentz factor

The energy E of a photon of wavelength λ is

E = hc/λ, where h is the Planck’s constant 6.6 x 10⁻³⁴ J.s and c being the speed of light in vacuum 3 x 108m/s

The momentum p of a photon of wavelenght λ is,

P = h/λ

If the electron is moving, it will start the interaction with some momentum and energy already. Momentum of the electron and photon in the initial and final state is

p(pi) + p(ei) = p(pf) + p(ef), equation 1, where p refers to momentum and the e and p in the brackets refer to proton and electron respectively

The momentum of the photon in the initial state is,

p(pi) = h/λ(i)

The momentum of the electron in the initial state is,

p(ei) = y(i)mu(i)

The momentum of the electron in the final state is

p(ef) = y(f)mu(f)

Since the electron starts off going in the negative direction, that momentum will be negative, along with the photon’s momentum after the collision

Rearranging the equation 1 , we get

p(pi) – p(ei) = -p(pf) +p(ef)

Substitute h/λ(i) for p(pi) , h/λ(f) for p(pf) , y(i)mu(i) for p(ei), y(f)mu(f) for p(ef) in the equation 1 and solve

h/λ(i) – y(i)mu(i) = -h/λ(f) – y(f)mu(f), equation 2

Next write out the energy conservation equation and expand it

E(pi) + E(ei) = E(pf) + E(ei)

Kinetic energy of the electron and photon in the initial state is

E(p) + E(ei) = E(ef), equation 3

The energy of the electron in the initial state is

E(pi) = hc/λ(i)

The energy of the electron in the final state is

E(pf) = hc/λ(f)

Energy of the photon in the initial state is

E(ei) = y(i)mc2, where y(i) is the frequency of the photon int the initial state

Energy of the electron in the final state is

E(ef) = y(f)mc2

Substitute hc/λ(i) for E(pi), hc/λ(f) for E(pf), y(i)mc² for E(ei) and y(f)mc² for E(ef) in equation 3

Hc/λ(i) + y(i)mc² = hc/λ(f) + y(f)mc², equation 4

Solve the equation for h/λ(f)

h/λ(i) + y(i)mc = h/λ(f) + y(f)mc

h/λ(f) = h/lmda(i) + (y(i) – y(f)c)m

Substitute h/λ(i) + (y(i) – y(f)c)m for h/λ(f)  in equation 2 and solve

h/λ(i) -y(i)mu(i) = -h/λ(f) + y(f)mu(f)

h/λ(i) -y(i)mu(i) = -h/λ(i) + (y(f) – y(i))mc + y(f)mu(f)

Rearrange to get all λ(i) terms on one side, we get

2h/λ(i) = m[y(i)u(i) +y(f)u(f) + (y(f) – y(i)c)]

λ(i) = 2h/[m{y(i)u(i) + y(f)u(f) + (y(f) – y(i))c}]

λ(i) = 2h/[m.c{y(i)(u(i)/c) + y(f)(u(f)/c) + (y(f) – y(i))}]

Calculate the Lorentz factor using u(i) = 0.8c for y(i) and u(i) = 0.6c for y(f)

y(i) = 1/[√[1 – (0.8c/c)²] = 5/3

y(f) = 1/√[1 – (0.6c/c)²] = 1.25

Substitute 6.63 x 10⁻³⁴ J.s for h, 0.511eV/c2 = 9.11 x 10⁻³¹ kg for m, 5/3 for y(i), 0.8c for u(i), 1.25 for y(f), 0.6c for u(f), and 3 x 10⁸ m/s for c in the equation derived for λ(i)

λ(i) = 2h/[m.c{y(i)(u(i)/c) + y(f)(u(f)/c) + (y(f) – y(i))}]

λ(i) = 2(6.63 x 10-34)/[(9.11 x 10-31)(3 x 108){(5/3)(0.8) + (1.25)(0.6) + ((1.25) – (5/3))}]

λ(i) = 2.91 x 10⁻¹² m

So, the initial wavelength of the photon was 2.91 x 10-12 m

Energy of the incoming photon is

E(pi) = hc/λ(i)

E(pi) = (6.63 x 10⁻³⁴)(3 x 10⁸)/(2.911 x 10⁻¹²) = 6.833 x 10⁻¹⁴ = 6.8 x 10⁻¹⁴

So the energy of the photon is 6.8 x 10⁻¹⁴ J

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Nearly 40 trillion kilometers, or 4.4 light-years, separate us from Alpha Centauri. The NASA-Germany Helios probes, the fastest spacecraft to date to be launched into orbit, flew at a speed of 250,000 kilometers per hour. The probes would need 18,000 years to travel at such pace to arrive at the sun's nearest neighbor. The calculations reveal that it is almost impossible to reach the nearest star in a human lifetime, even with the most futuristic technologies.

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