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Fed [463]
3 years ago
5

A 0.5 kg block of aluminum (caluminum=900j/kg⋅∘c) is heated to 200∘c. the block is then quickly placed in an insulated tub of co

ld water at 0∘c (cwater=4186j/kg⋅∘c) and sealed. at equilibrium, the temperature of the water and block are measured to be 20∘c. part a if the original experiment is repeated with a 1.0 kg aluminum block, what is the final temperature of the water and block?

Physics
2 answers:
garri49 [273]3 years ago
7 0

The final temperature of the water and block is 36°C

<h3>Further explanation</h3>

Specific Heat Capacity is the amount of energy needed to raise temperature of 1 kg body for 1°C.

\large {\boxed{Q = m \times c \times \Delta t} }

<em>Q = Energy ( Joule )</em>

<em>m = Mass ( kg ) </em>

<em>c = Specific Heat Capacity ( J / kg°C ) </em>

<em>Δt = Change In Temperature ( °C )</em>

Let us now tackle the problem!

<u>Given:</u>

mass of aluminium in the first experiment = m₁ = 0.5 kg

specific heat capacity of aluminium = c₁ = 900 J/kg°C

initial temperature of aluminium = t = 200°C

specific heat capacity of water = c₂ = 4186 J/kg°C

final temperature of the first experiment = t₁ = 20°C

mass of aluminium in the second experiment = m₂ = 1.0 kg

<u>Unknown:</u>

final temperature of the second experiment = t₂ = ?

<u>Solution:</u>

<h2>First Experiment :</h2>

Firstly , we would like to calculate the mass of the water using Conservation of Energy as shown below

Q_{lost} = Q_{gained}

Q_{aluminium} = Q_{water}

m_1 \times c_1 \times (t - t_1) = m \times c_2 \times (t_1 - 0)

0.5 \times 900 \times (200 - 20) = m \times 4186 \times (20 - 0) )

81000 = 83720~m

m = \frac{2025}{2093} ~ kg

<h2>Second Experiment :</h2>

Using the same formula , we could calculate the final temperature of the water and block in the second experiment

Q_{lost} = Q_{gained}

Q_{aluminium} = Q_{water}

m_2 \times c_1 \times (t - t_2) = m \times c_2 \times (t_2 - 0)

1.0 \times 900 \times (200 - t_2) = \frac{2025}{2093} \times 4186 \times (t_2 - 0) )

1.0 \times 900 \times (200 - t_2) = 4050 ~ t_2

180000 - 900 ~ t_2 = 4050 ~ t_2

4950 ~ t_2 = 180000

t_2 = \frac{180000}{4950}

t_2 \approx 36^oC

<h3>Learn more</h3>
  • Efficiency of Engine : brainly.com/question/5597682
  • Flow of Heat : brainly.com/question/3010079
  • Difference Between Temperature and Heat : brainly.com/question/3821712

<h3>Answer details </h3>

Grade: College

Subject: Physics

Chapter: Thermal Physics

Keywords: Heat , Temperature , Block , Aluminium , Ice , Cold , Water

Alex_Xolod [135]3 years ago
4 0

To solve this problem, we should recall the law of conservation of energy. That is, the heat lost by the aluminium must be equal to the heat gained by the cold water. This is expressed in change in enthalpies therefore:

- ΔH aluminium = ΔH water

where ΔH = m Cp (T2 – T1)

The negative sign simply means heat is lost. Therefore we calculate for the mass of water (m):

- 0.5 (900) (20 – 200) = m (4186) (20 – 0)

m = 0.9675 kg

 

Using same mass of water and initial temperature, the final temperature T of a 1.0 kg aluminium block is:

- 1 (900) (T – 200) = 0.9675 (4186) (T – 0)

- 900 T + 180,000 = 4050 T

4950 T = 180,000

T = 36.36°C

 

The final temperature of the water and block is 36.36°C

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A 125-kg astronaut (including space suit) acquires a speed of 2.50 m/s by pushing off with her legs from a 1900-kg space capsule
ryzh [129]

(a) 0.165 m/s

The total initial momentum of the astronaut+capsule system is zero (assuming they are both at rest, if we use the reference frame of the capsule):

p_i = 0

The final total momentum is instead:

p_f = m_a v_a + m_c v_c

where

m_a = 125 kg is the mass of the astronaut

v_a = 2.50 m/s is the velocity of the astronaut

m_c = 1900 kg is the mass of the capsule

v_c is the velocity of the capsule

Since the total momentum must be conserved, we have

p_i = p_f = 0

so

m_a v_a + m_c v_c=0

Solving the equation for v_c, we find

v_c = - \frac{m_a v_a}{m_c}=-\frac{(125 kg)(2.50 m/s)}{1900 kg}=-0.165 m/s

(negative direction means opposite to the astronaut)

So, the change in speed of the capsule is 0.165 m/s.

(b) 520.8 N

We can calculate the average force exerted by the capsule on the man by using the impulse theorem, which states that the product between the average force and the time of the collision is equal to the change in momentum of the astronaut:

F \Delta t = \Delta p

The change in momentum of the astronaut is

\Delta p= m\Delta v = (125 kg)(2.50 m/s)=312.5 kg m/s

And the duration of the push is

\Delta t = 0.600 s

So re-arranging the equation we find the average force exerted by the capsule on the astronaut:

F=\frac{\Delta p}{\Delta t}=\frac{312.5 kg m/s}{0.600 s}=520.8 N

And according to Newton's third law, the astronaut exerts an equal and opposite force on the capsule.

(c) 25.9 J, 390.6 J

The kinetic energy of an object is given by:

K=\frac{1}{2}mv^2

where

m is the mass

v is the speed

For the astronaut, m = 125 kg and v = 2.50 m/s, so its kinetic energy is

K=\frac{1}{2}(125 kg)(2.50 m/s)^2=390.6 J

For the capsule, m = 1900 kg and v = 0.165 m/s, so its kinetic energy is

K=\frac{1}{2}(1900 kg)(0.165 m/s)^2=25.9 J

3 0
3 years ago
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