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Anni [7]
3 years ago
10

A gas has an initial volume of 212 cm^3 at a temperature of 293 K and a pressure of 0.98 atm. What is the final pressure of the

gas if the volume decreases to 196 cm^3 and the temperature of the gas increases to 308 K?
a. 0.86 atm
b. 0.95 atm
c. 1.0 atm
d. 1.1 atm
Physics
1 answer:
MatroZZZ [7]3 years ago
8 0
For this we use general equation for gases. Our variables represent:

p- pressure
v-volume
t- temperature

P1V1/T1 = P2V2/T2

in this equation we know:
P1,V1 and T1, T2 and V2. 
We have one equation and 1 unknown variable.

P2 = T2P1V1/T1V2 = 1.1atm
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Two transverse waves travel along the same taut string inopposite directions. the waves are described by following equations use
Umnica [9.8K]

Answer: y'=2Asin(kx)cos(wt)

Explanation:

Let y1=A sin (kx + wt) be the first wave

y2=A sin (kx - wt) be the second wave in the opposite direction (which we showed by putting a negative sign between the terms kx and wt)

Please do note that both wave have the same attributes (that's Amplitude, wave number and angular frequency) because they are formed on the same medium by the same source just that their directions are opposite.

By super imposing these 2 waves, we have a resulting singular wave representing both wave (law of superimposition) with a resulting value of vertical displacement y'.

Thus y' = y1 + y2.

Let us do the math.

y'=A sin (kx + wt) + A sin (kx - wt)

By factoring A out, we have that

y' = A [ sin (kx + wt) + sin (kx - wt)]

For simplicity let us use the substitution

Let (kx + wt) = a and (kx - wt) =b

Hence we have that

y' = A [sin a + sin b].

From trigonometric ratio

sin a + sin b = 2sin[(a+b)/2] * cos [(a - b)/2]

By recalling that (kx + wt) = a and (kx - wt) =b

sin a + sin b = 2sin [(kx +wt +kx-wt) /2] * cos [(kx +wt - (kx-wt))/2]

Thus we have that

sin a + sin b = 2sin [(kx+wt+kx-wt)/2] * cos[(kx+wt-kx+wt)/2]

By collecting like terms in the bracket we have that

sin a + sin b = 2sin[2kx/2] * cos [2wt/2]

By dividing

sin a + sin b = 2sin(kx) cos(wt)

Now let us get the final resultant vertical displacement (y')

Recall that

y' = A [sin a + sin b]. and we already deduced that

sin a + sin b = 2sin(kx) cos(wt)

Finally,

y' = A [2sin(kx) cos(wt)] which is

y'=2Asin(kx)cos(wt)...... Final answer

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