Physics, 16.12.2019 16:31 hmskevinjacobo5471

Aplayer bounces a basketball on the floor, compressing it to 80.0 % of its original volume. the air (assume it is essentially n2 gas) inside the ball is originally at a temperature of 20.0 ∘c and a pressure of 2.00 atm. the ball's diameter is 23.9 cm. by how much does the internal energy of the air change between the ball's original state and the maximum compression?

Answers: 3

Show answers

Answers

Answer from: jbrown76241

292.95 J

Explanation:

change in internal energy= Heat transfer - work done

ΔU =Q -PΔV

Here, Q = 0 as there is no heat transfer.

P =2.00 atm = 2.00 × 101235 Pa = 202470 Pa

ΔV = final volume - initial volume = 0.8 V -V = -0.2 V

where V is the initial volume.

Volume of a spherical ball, $V = \frac{4}{3}\pi r^3$

r = d/2 = 23.9 cm / 2 = 0.12 m

$V = \frac{4}{3}\times 3.14 \times (0.12m)^3= 7.23\times10^{-3}m^3$

$\DeltaU = -P\DeltaV = - 202470 Pa \times -0.2 \times 7.23\times10^{-3}m^3=292.95 J$

Hence, internal energy would change by 292.95 J.

Answer from: krystalhurst97

The change in internal energy after the ball is compressed is $\fbox{289.7\,{\text{J}}}$ .

Further explanation:

Change in energy is done on the cost of its internal energy which is given by the first law of thermodynamics.

Given:

The new volume of the ball is 0.8 times the original volume.

The pressure inside the ball is 2atm.

The diameter of the ball is 23.9cm.

Concept used:

Law of Conservation of Energy state that “Energy can neither be created nor be destroyed but only it can be transferred from one to another form and also called first law of thermodynamics.

The first law of thermodynamics state that "the amount of change in internal energy $\Delta U$ of one system is expressed as sum of heat that transferring across its boundaries of the system and work done on system by surroundings":

$\Delta U = Q + W$ …… (1)

The expression for the work done is given as.

$W = P\Delta V$

Here, $\Delta V$ is the change in volume and P is the pressure.

In this system there is no heat transfer i.e. Q = 0 .

Substitute $P\Delta V$ for W and for Q in equation (1).

$\fbox{\begin\\\Delta U = P\Delta V\end{minispace}}$

The final expression reduces as.

$\Delta U = P\left( {{V_2} - {V_1}} \right)$ …… (2)

Here, ${V_1}$ is the original volume, ${V_2}$ is the compressed volume and $\Delta U$ is the change in internal energy.

The expression for the volume of sphere is given as.

${V_1} = \dfrac{4}{3}\pi {r_1}^3$ …… (3)

Here, ${r_1}$ is the radius of ball.

Substitute $\left( {\frac{{23.9}}{2}} \right){\text{cm}}$ for r_1 in equation (3).

$\begin{aligned}{V_1}&=\frac{4}{3}\pi {\left( {\frac{{23.9\,{\text{cm}}}}{2}} \right)^3}\\&=\frac{4}{3}\pi {\left( {\frac{{23.9\,{\text{cm}}}}{2}\left( {\frac{{1\,{\text{m}}}}{{100\,{\text{cm}}}}} \right)} \right)^3} \\&=7.15\,{{\text{m}}^{\text{3}}}\\ \end{aligned}$

Substitute $0.8{V_1}$ for ${V_2}$ , $2\,{\text{atm}}$ for P and $7.15\,{{\text{m}}^{\text{3}}}$ for ${V_1}$ in equation (2).

$\begin{aligned}\Delta U&=\left( {2\,{\text{atm}}} \right)\left( {0.8{V_1} - {V_1}} \right) \\&=\left({2\,{\text{atm}}\left( {\frac{{{\text{101325}}\,{\text{Pa}}}}{{1\,{\text{atm}}}}} \right)} \right)\left( {0.2{V_1}} \right)\\&=\left( {202650} \right)\left( {0.2\left( {7.15\,{{\text{m}}^{\text{3}}}} \right)} \right)\\&=289.7\,{\text{J}} \\ \end{aligned}$

Thus, the change in internal energy of the ball is $\fbox{289.7\,{\text{J}}}$ .

Learn more:

1. Example of energies .

2. Motion under friction .

3. Average translational kinetic energy .

Answer Details:

Grade: College

Subject: Physics

Chapter: Heat and Thermodynamics

Keywords:

Energy, heat, work, first law of thermodynamics, conservation of energy, volume, mass, change in volume, heat transfer, compression, system, surrounding, 289.7J, 290J, 7.15m^3.

Answer from: Quest

e/c, where e is its total energy

Answer from: Quest

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2

Another question on Physics

Physics, 22.06.2019 12:00

This is for my 8th grade science class, i really don’t understand. can someone me? , lol.

Answers: 1

Answer

Physics, 22.06.2019 12:00

Explain what happens at the saturation point when adding salt to water at room temperature.

Answers: 3

Answer

Physics, 22.06.2019 17:30

This chart shows characteristics of three different types of waves. which statement is best supported by the information in the chart? wave x and wave y are mechanical waves, and wave z is an electromagnetic wave. wave x and wave y are electromagnetic waves, and wave z is a mechanical wave. wave x and wave z are electromagnetic waves, and wave y is a mechanical wave. wave x and wave z are mechanical waves, and wave y is an electromagnetic wave.

Answers: 1

Answer

Physics, 22.06.2019 17:30

Which basic property determines a colored light's placement on the spectrum of visible light? a. speed b. frequency c. amplitude d. velocity

Answers: 3

Answer

You know the right answer?

Aplayer bounces a basketball on the floor, compressing it to 80.0 % of its original volume. the air...

Questions