Burns produced by steam at 100°C are much more severe than those produced by the same mass of 100°C water. Calculate the quantity of heat in (Cal or kcal) that must be removed from 6.1 g of 100°C steam to condense it and lower its temperature to 46°C. Specific heat of water = 1.00 kcal/(kg · °C); heat of vaporization = 539 kcal/kg; specific heat of human flesh = 0.83 kcal/(kg · °C).

Answers

Answer 1
Answer:

Final answer:

To calculate the quantity of heat that must be removed from 6.1 g of 100°C steam, we need to consider both the change in temperature and the phase change from steam to liquid. The specific heat of water is used to calculate the heat required to lower the temperature, while the heat of vaporization is used to calculate the heat required to condense the steam. Adding these two heat values together gives us the total amount of heat that must be removed from the steam, which is approximately 3.61164 kcal.

Explanation:

When steam at 100°C condenses and its temperature is lowered to 46°C, heat must be removed from the steam. To calculate the amount of heat, we can use the specific heat of steam and the latent heat of vaporization. First, we calculate the heat required to lower the temperature of the steam from 100°C to 46°C using the specific heat of water. We then calculate the heat required to condense the steam using the latent heat of vaporization. Finally, we add these two heat values together to obtain the total amount of heat that must be removed from the steam.

Given:

  • Mass of steam = 6.1 g
  • Temperature change = 100°C - 46°C = 54°C
  • Specific heat of water = 1.00 kcal/(kg · °C)
  • Heat of vaporization = 539 kcal/kg


Calculations:

  1. Heat required to lower the temperature of the steam:
    Q1 = mass × specific heat × temperature change
     = 6.1 g × (1.00 kcal/(kg · °C) ÷ 1000 g) × 54°C
  2. Heat required to condense the steam:
    Q2 = mass × heat of vaporization
      = 6.1 g × (539 kcal/kg ÷ 1000 g)
  3. Total heat required:
    Q = Q1 + Q2

Calculation:

  1. Q1 = 0.32874 kcal
  2. Q2 = 3.2829 kcal
  3. Q = Q1 + Q2 = 0.32874 kcal + 3.2829 kcal = 3.61164 kcal


Therefore, the quantity of heat that must be removed from 6.1 g of 100°C steam to condense it and lower its temperature to 46°C is approximately 3.61164 kcal.

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Answer 2
Answer:

Final answer:

To condense and cool 6.1 g of 100°C steam to 46°C, 3.2879 kcal must be removed for condensation, and 0.3304 kcal for cooling, for a total of 3.6183 kcal.

Explanation:

Calculating the Quantity of Heat for Condensation and Cooling

To calculate the quantity of heat that must be removed from 6.1 g of 100°C steam to condense it and lower its temperature to 46°C, we need to consider two processes: condensation and cooling. For condensation, we use the heat of vaporization, and for cooling, we use the specific heat of water.

  1. Calculate the heat released during condensation of steam into water at 100°C:
     Heat = mass × heat of vaporization
     Heat (in kcal) = (6.1 g) × (539 kcal/kg) × (1 kg / 1000 g)
     Heat = 3.2879 kcal
  2. Calculate the heat released when the water cools from 100°C to 46°C:
     Heat = mass × specific heat × change in temperature
     Heat (in kcal) = (6.1 g) × (1.00 kcal/kg°C) × (1 kg / 1000 g) × (100°C - 46°C)
     Heat = 0.3304 kcal

Total heat removed is the sum of the heat from both steps: 3.2879 kcal + 0.3304 kcal = 3.6183 kcal.

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Answers

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What kind of exercise should you do when you're cooling down after an
intense workout?

Answers

Answer:

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Explanation:

It's kinda resting

Answer:

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Two children, each with a mass of 25.4 kg, are at fixed locations on a merry-go-round (a disk that spins about an axis perpendicular to the disk and through its center). One child is 0.78 m from the center of the merry-go-round, and the other is near the outer edge, 3.14 m from the center. With the merry-go-round rotating at a constant angular speed, the child near the edge is moving with translational speed of 11.5 m/s.a. What is the angular speed of each child?
b. Through what angular distance does each child move in 5.0 s?
c. Through what distance in meters does each child move in 5.0 s?
d. What is the centripetal force experienced by each child as he or she holds on?
e. Which child has a more difficult time holding on?

Answers

Answer:

a) ω₁ = ω₂ = 3.7 rad/sec

b) Δθ₁ = Δθ₂ = 18.5 rad

c) d₁ = 14.5 m  d₂ = 57.5 m

d) Fc1 = 273.9 N Fc2 = 1069.8 N

e) The boy near the outer edge.

Explanation:

a)

  • Since the merry-go-round is a rigid body, any point on it rotates at the same angular speed.
  • However, linear speeds of points at different distances from  the center, are different.
  • Applying the definition of angular velocity, and the definition of angle, we can write the following relationship between the angular and linear speeds:

       v = \omega*r (1)

  • Since we know the value of v for the child near the outer edge, and the value of r for this point, we can find the value of the angular speed, as follows:

       \omega = (v_(out) )/(r_(out) ) = (11.5m/s)/(3.14m) = 3.7 rad/sec  (2)

  • As we have already said, ωout = ωin = 3.7 rad/sec

b)

  • Since the angular speed is the same for both childs, the angle rotated in the same time, will be the same for both also.
  • Applying the definition of angular speed, as the rate of change of the angle rotated with respect to time, we can find the angle rotated (in radians) as follows:
  • \Delta \theta = \omega * t = 3.7 rad/sec* 5.0 sec = 18.5 rad  (3)

        ⇒  Δθ₁ = Δθ₂ = 18.5 rad.

c)

  • The linear distance traveled by each child, will be related with the linear speed of them.
  • Knowing the value of the angular speed, and the distance from each boy to the center, we can apply (1) in order to get the linear speeds, as follows:

       v_(inn) = \omega * r_(inn) = 3.7 rad/sec * 0.78 m = 2.9 m/s  (4)

      vout is a given of the problem ⇒ vout = 11. 5 m/s

  • Applying the definition of linear velocity, we can find the distance traveled by each child, as follows:

       d_(inn) = v_(inn) * t = 2.9m/s* 5.0 s = 14.5 m (5)

      d_(out) = v_(out) * t = 11.5 m/s* 5.0 s = 57.5 m (6)

d)

  • The centripetal force experienced by each child is the force that keeps them on a circular movement, and can be written as follows:

       F_(c) = m*(v^(2))/(r)  (7)

  • Replacing by the values of vin and rin, since m is a given, we can find Fcin (the force on the boy closer to the center) as follows:

      F_(cin) = m*(v_(in)^(2))/(r_(in)) = 25.4 kg* ((2.9m/s)^(2) )/(0.78m) = 273.9 N (8)

  • In the same way, we get Fcout (the force on the boy near the outer edge):

      F_(cout) = m*(v_(out)^(2))/(r_(out)) = 25.4 kg* ((11.5m/s)^(2) )/(3.14m) = 1069.8 N (9)

e)

  • The centripetal force that keeps the boys in a circular movement, is not a different type of force, and in this case, is given by the static friction force.
  • The maximum friction force is given by the product of the coefficient of static friction times the normal force.
  • Since the boys are not accelerated in the vertical direction, the normal force is equal and opposite to the force due to gravity, which is the weight.
  • As both boys have the same mass, the normal force is also equal.
  • This means that for both childs, the maximum possible static friction force, is the same, and given by the following expression:
  • F_(frs)  = \mu_(s) * m* g  (10)
  • If this force is greater than the centripetal force, the boy will be able to hold on.
  • So, as the centripetal force is greater for the boy close to the outer edge, he will have a more difficult time holding on.

(a) How fast and in what direction must galaxy A be moving if an absorption line found at 550 nm (green) for a stationary galaxy is shifted to 450 nm (blue) for A? (b) How fast and in what direction is galaxy B moving if it shows the same line shifted to 700 nm (red)?

Answers

Explanation:

For Part (a)

Since the apparent wavelength decreases hence galaxy moving towards the stationary observer.

Δλ/λ=v/c

=(v)/(c)\n v=(550-450)/(550)*3*10^(8)\n v=5.4545*10^(7)m/s

For Part (b)

Since the apparent wavelength increases hence galaxy moving towards the stationary observer.

Δλ/λ=v/c

=(v)/(c)\n v=(700-550)/(550)*3*10^(8)\n v=8.1818*10^(7)m/s

How much work would it take to push two protons very slowly from a separation of 2.00×10−10 m (a typical atomic distance) to 3.00×10−15 m (a typical nuclear distance)?

Answers

Electric potential is the amount of work needed to move a unit charge from a point to a specific point against an electric field. The work would it take to push two protons will be 7.7×10⁻¹⁴.

What is electric potential?

Electric potential is the amount of work needed to move a unit charge from a point to a specific point against an electricfield.

The given data in the problem is;

q is the charge= 1.6 ×10⁻¹⁹ C

V is the electric potential

r₁ is the first separation distance= 2.00×10−10 m

r₂ is the second  separation distance=  3.00×10−15 m

The electric potential generated by the proton at rest at the two points, using the formula:

Firstly the electric potential at loction 1

\rm V=(Kq)/(r)  \n\n v_i= 9* 10^9 * (1.6*10^(-19))/(2.0*10^(-10))

The electric potential at loction 2

V_f = 9 * 10^9 (1.6 * 10^(-19))/(3.0*10^(-15)) \n\n \rm v_f= 4.8 *10^5 \ V

The product of difference of electric potential and charge is defined as the workdone.

\rm W= q \triangle V \n\n \rm W= 1.6 * 10^-19 *( 4.8*10^5 -7.2)  \n\n \rm W= 7.7 * 10^(-14)

Hence the work would it take to push two protons will be 7.7×10⁻¹⁴.

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We can visualize the problem in another way, which is equivalent but easier to solve: let's imagine we hold one proton in the same place, and we move the other proton from a distance of 2.00×10−10 m to a distance of 3.00×10−15 m from the first proton. How much work is done?

The work done is equal to the electric potential energy gained by the proton:

W=q \Delta V

where q=1.6 \cdot 10^(-19)C is the charge of the proton and \Delta V is the potential difference between the final position and the initial position of the proton. To calculate this \Delta V, we must calculate the electric potential generated by the proton at rest at the two points, using the formula:

V=k(Q)/(r)

where k=9.0 \cdot 10^9 N m^2 C^(-2) is the Coulomb constant and Q is the proton charge. Substituting the initial and final distance of the second proton, we find

V_i = (9.0 \cdot 10^9 )(1.6 \cdot 10^(-19))/(2.0 \cdot 10^(-10))=7.2 V

V_f = (9.0 \cdot 10^9 )(1.6 \cdot 10^(-19))/(3.0 \cdot 10^(-15))=4.8 \cdot 10^5 V

Therefore, the work done is

W=q \Delta V=(1.6 \cdot 10^(-19)C)(4.8 \cdot 10^5 V-72 V)=7.7 \cdot 10^(-14) J

In an 8.00km race, one runner runs at a steady 11.8 km/hr and another runs at 15.0 km/hr. How far from the finish line is the slower runner when the faster runner finishes the race?

Answers

Answer:

The slower runner is 1.71 km from the finish line when the fastest runner finishes the race.

Explanation:

Given;

the speed of the slower runner, u₁ = 11.8 km/hr

the speed of the fastest runner, u₂ = 15 km/hr

distance, d = 8 km

The time when the fastest runner finishes the race is given by;

Time = (Distance )/(speed)\n\nTime = (8)/(15) \n\nTime = 0.533 \ hr

The distance covered by the slower runner at this time is given by;

d₁ = u₁ x 0.533 hr

d₁ = 11.8 km/hr x 0.533 hr

d₁ = 6.29 km

Additional distance (x) the slower runner need to finish is given by;

6.29 km + x = 8km

x = 8 k m - 6.29 km

x = 1.71 km

Therefore, the slower runner is 1.71 km from the finish line when the fastest runner finishes the race.

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