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3 years ago

8

180 cm3 of hot tea at 97 °C are poured into a very thin paper cup with 20 g of crushed ice at 0 °C. Calculate the final temperat

ure of the "ice tea."(Hint: think about two processes: melting the ice into liquid and (maybe) warming the melted ice—now liquid.)

1 answer:

Zolol [24]3 years ago

8 0

Answer : The final temperature of the mixture is $91.9^oC$

Explanation :

First we have to calculate the mass of water.

Mass = Density × Volume

Density of water = 1.00 g/mL

Mass = 1.00 g/mL × 180 cm³ = 180 g

In this problem we assumed that heat given by the hot body is equal to the heat taken by the cold body.

$q_1=-q_2$

$m_1\times c_1\times (T_f-T_1)=-m_2\times c_2\times (T_f-T_2)$

where,

$c_1$ = specific heat of hot water (liquid) = $4.18J/g^oC$

$c_2$ = specific heat of ice (solid)= $2.10J/g^oC$

$m_1$ = mass of hot water = 180 g

$m_2$ = mass of ice = 20 g

$T_f$ = final temperature of mixture = ?

$T_1$ = initial temperature of hot water = $97^oC$

$T_2$ = initial temperature of ice = $0^oC$

Now put all the given values in the above formula, we get

$(180g)\times (4.18J/g^oC)\times (T_f-97)^oC=-(20g)\times 2.10J/g^oC\times (T_f-0)^oC$

$T_f=91.9^oC$

Therefore, the final temperature of the mixture is $91.9^oC$

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4 years ago

Miss Piggy is exercising her vocal chords by matching the frequency f = 686 Hz of her speaker 4 m away. Where should Kermit sit

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Answer:

$z=\frac{2n+1}{8}$ for $n=0,1,2,3,...,15$

Where z=0 m is the position of Miss Piggy and z=4 m is the position of the speaker.

Explanation:

Assuming that Miss Piggy emits a sound wave that is in phase with the speaker, and that z=0 is the position of Miss Piggy and z=4 is the position of the speaker, we would have a superposition of two traveling sound waves. Furthermore let's assume that both waves have the same amplitude. The total resulting wave will be given by:

$\psi(t,z)=A\cos(\omega t-kz)+A\cos(\omega t +kz)$ where $\omega$ is the angular frequency of the traveling wave and $k$ is the wave number defined as $k=\frac{2\pi}{\lambda}$ . $\lambda$ is the wavelength of both traveling waves (they have the same wavelength because they have the same frequency). $\lambda=\frac{v}{f}$ where v is the speed of sound.

By using the trigonometric identity $2\cos(A)\cos(B)=\cos(A+B)+\cos(A-B)$ we can rewrite $\psi (t,z)$ as

$\psi (t,z)=2A\cos(\omega t)\cos(kz)$ .

In order for the resulting wave to have maximum destructive interference, that is to be zero for any time t, we need to have

$\cos(kz)=0$

$\implies kz=(2n+1)\cdot \frac{\pi}{2}\implies z=(2n+1)\frac{\pi}{2k}=(2n+1)\frac{\pi}{2}\frac{\lambda}{2\pi}=(2n+1)\cdot \frac{\lambda}{4}$

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3 years ago

A 0.200 H inductor is connected in series with a 88.0 Ω resistor and an ac source. The voltage across the inductor is vL=−(12.0V

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Answer:

a. (VL)R/ωL[1 - cos[ωt]] = (10.84 V)[1 - cos[(487rad/s)t]]

b. 1.084 mV

Explanation:

a. Since it is a series circuit, the current in the inductor is the same as the current in the resistor.

Now, the voltage across the inductor vL = -Ldi/dt.

So, the current, i = -1/L∫vLdt.

Now, vL = −(12.0V)sin[(487rad/s)t] and L = 0.200 H

Substituting these into i, we have

i = -1/L∫vLdt

= -1/0.200H∫[−(12.0V)sin[(487rad/s)t]]dt.

= -[−(12.0V)]/0.200H∫[sin[(487rad/s)t]]dt.

= 60V/H∫[sin[(487rad/s)t]]dt

Integrating i, we have

i = 60V/H ÷ [(487rad/s)[-cos[(487rad/s)t]] + C

at t = 0, i(0) = 0

0 = 60V/H ÷ [(487rad/s)[-cos[(487rad/s)× 0]] + C

0 = 60V/H ÷ [(487rad/s)[-cos[0]] + C

0 = 60V/H ÷ [(487rad/s)[-1]+ C

C = 60V/H ÷ [(487rad/s)

So, i = 60V/H ÷ [(487rad/s)[-cos[(487rad/s)t]] + 60V/H ÷ [(487rad/s)

i = 60V/H ÷ [(487rad/s)[1 - cos[(487rad/s)t]]

i = (0.123A)[1 - cos[(487rad/s)t]] = VL/ωL[1 - cos[ωt]] where ω = 487rad/s and VL = 12.0 V and L = 0.200 H

So, the voltage across the resistor vR = iR where R = resistance of resistor = 88.0 Ω

So, vR = iR = VL/ωL[1 - cos[ωt]] × R = (VL)R/ωL[1 - cos[ωt]]

= (0.123A)[1 - cos[(487rad/s)t]] × 88.0 Ω

= (10.84 V)[1 - cos[(487rad/s)t]]

b. vR at t = 2.00 ms = 0.002 s

So, vR = (10.84 V)[1 - cos[(487rad/s)(0.002)]]

= (10.84 V)[1 - cos[0.974]]

= (10.84 V)[1 - 0.9999]

= (10.84 V)(0.0001)

= 0.001084

= 1.084 mV

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