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Evgen [1.6K]
3 years ago
10

The quartz crystal used in an electric watch vibrates with a frequency of 32,768 Hz. What is the period of the crystal's motion?

Physics
1 answer:
Elan Coil [88]3 years ago
8 0

Answer:

Time period, T=3.05\times 10^{-5}\ s

Explanation:

Given that,

The quartz crystal used in an electric watch vibrates with a frequency of 32,768 Hz, f = 32768 Hz

We need to find the period of the crystal's motion. The relationship between the frequency and the time period is given by :

T=\dfrac{1}{f}

T is the time period of the crystal's motion.

Time period is given by :

T=\dfrac{1}{32768}

T=3.05\times 10^{-5}\ s

So, the time period of the crystal's motion is 3.05\times 10^{-5}\ s. Hence, this is the required solution.

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A mole of ideal gas expands at T=27 °C. The pressure changes from 20 atm to 1 atm. What’s the work that the gas has done and wha
Airida [17]

Answer:

  • The work made by the gas is 7475.69 joules
  • The heat absorbed is 7475.69 joules

Explanation:

<h3>Work</h3>

We know that the differential work made by the gas  its defined as:

dW =  P \ dv

We can solve this by integration:

\Delta W = \int\limits_{s_1}^{s_2}\,dW = \int\limits_{v_1}^{v_2} P \ dv

but, first, we need to find the dependence of Pressure with Volume. For this, we can use the ideal gas law

P \ V = \ n \ R \ T

P = \frac{\ n \ R \ T}{V}

This give us

\int\limits_{v_1}^{v_2} P \ dv = \int\limits_{v_1}^{v_2} \frac{\ n \ R \ T}{V} \ dv

As n, R and T are constants

\int\limits_{v_1}^{v_2} P \ dv = \ n \ R \ T \int\limits_{v_1}^{v_2} \frac{1}{V} \ dv

\Delta W= \ n \ R \ T  \left [ ln (V) \right ]^{v_2}_{v_1}

\Delta W = \ n \ R \ T  ( ln (v_2) - ln (v_1 )

\Delta W = \ n \ R \ T  ( ln (v_2) - ln (v_1 )

\Delta W = \ n \ R \ T  ln (\frac{v_2}{v_1})

But the volume is:

V = \frac{\ n \ R \ T}{P}

\Delta W = \ n \ R \ T  ln(\frac{\frac{\ n \ R \ T}{P_2}}{\frac{\ n \ R \ T}{P_1}} )

\Delta W = \ n \ R \ T  ln(\frac{P_1}{P_2})

Now, lets use the value from the problem.

The temperature its:

T = 27 \° C = 300.15 \ K

The ideal gas constant:

R = 8.314 \frac{m^3 \ Pa}{K \ mol}

So:

\Delta W = \ 1 mol \ 8.314 \frac{m^3 \ Pa}{K \ mol} \ 300.15 \ K  ln (\frac{20 atm}{1 atm})

\Delta W = 7475.69 joules

<h3>Heat</h3>

We know that, for an ideal gas, the energy is:

E= c_v n R T

where c_v its the internal energy of the gas. As the temperature its constant, we know that the gas must have the energy is constant.

By the first law of thermodynamics, we know

\Delta E = \Delta Q - \Delta W

where \Delta W is the Work made by the gas (please, be careful with this sign convention, its not always the same.)

So:

\Delta E = 0

\Delta Q = \Delta W

7 0
3 years ago
An ocean wave has a frequency of 9 Hz and a speed of 18 m/s. What is the wavelength of this wave?
leonid [27]

Answer:

The answer is 2 because the formula is

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7 0
3 years ago
A 0.900-V potential difference is maintained across a 1.5m length of 2
Daniel [21]

Answer:

I = 6.42 A

Explanation:

Given that,

Potential difference, V = 0.9 V

Length of the wire, l = 1.5 m

Area of cross section, A=0.6\ mm^2=6\times 10^{-7}\ m^2

We need to find the current in the wire. Let I is current. We can find it using Ohm's law as follows :

V = IR

Where R is the resistance of the wire

I=\dfrac{V}{R}\\\\I=\dfrac{V}{\rho \dfrac{l}{A}}\\\\I=\dfrac{0.9}{5.6\times 10^{-8}\times \dfrac{1.5}{6\times 10^{-7}}}\\\\I=6.42\ A

So, the current in the wire is 6.42 A.

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How to find coefficient of lift from coefficient of pressure?
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A cube of iron (Cp = 0.450 J/g•°C) with a mass of 55.8 g is heated from 25.0°C to 49.0°C. How much heat is required for this pro
Rus_ich [418]
Q = mcΔT 
<span>q = 55.8g x 0.450J/gC x 23.5C </span>
<span>q = 590. J ................ to three significant digits

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.

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