Select the correct answer.

The pressure and volume of an expanding gas are related by the formula PV^b=C, where b and C are constants (this holds in adiaba

bazaltina [42]

The dP/dt of the adiabatic expansion is -42/11 kPa/min

<h3>How to calculate dP/dt in an adiabatic expansion?</h3>

An adiabatic process is a process in which there is no exchange of heat from the system to its surrounding neither during expansion nor during compression

Given b=1.5, P=7 kPa, V=110 cm³, and dV/dt=40 cm³/min

PVᵇ = C

Taking logs of both sides gives:

ln P + b ln V = ln C

Taking partial derivatives gives:

$\frac{1}{P}\frac{∂P}{∂t} + \frac{b}{V}\frac{∂V}{∂t} = 0$

Substitutituting the values b, P, V and dV/dt into the derivative above:

1/7 x dP/dt + 1.5/110 x 40 = 0

1/7 x dP/dt + 6/11 = 0

1/7 x dP/dt = - 6/11

dP/dt = - 6/11 x 7

dP/dt = -42/11 kPa/min

Therefore, the value of dP/dt is -42/11 kPa/min

Learn more about adiabatic expansion on:

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4 0

1 year ago

A box contains different colored paper clips. The probability of drawing two red paper clips from the box without replacement is

ivann1987 [24]

Answer: 5/14 which is choice B

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How I got this answer:

Define the following events

A = event of picking a red paper clip on the first selection

B = event of picking a red paper clip on the second drawing

Replacement is not made.

Now onto the probabilities for each

P(A) = 2/5 = 0.4 is given to us as this is simply the probability of picking red on the first try

P(A and B) = probability of both events A and B happeing simultaneously = 1/7

P(B|A) = probability event B occurs, given event A has occured

P(B|A) = probability of selecting red on second selection, given first selection is red (no replacement)

P(B|A) = P(A and B)/P(A)

P(B|A) = (1/7) / (2/5)

P(B|A) = (1/7) * (5/2)

P(B|A) = (1*5)/(7*2)

P(B|A) = 5/14

So if event A happens, then the chances of event B happening is 5/14

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A more concrete example:

If we had 15 paperclips, and 6 of them were red, then

P(A) = (# of red)/(# total) = 6/15 = 2/5

P(B|A) = (# of red left)/(# total left) = (6-1)/(15-1) = 5/14

P(A and B) = P(A)*P(B|A) = (2/5)*(5/14) = 10/70 = 1/7

7 0

3 years ago

Read 2 more answers

Which coordinate pair is a solution of the equation below?

Anni [7]

I think that the answer is b because if you substitute in (4,1) into x-5y=-1 you’ll get 4-5(1)=-1 which simplifies to -1=+1 which is a true statement. I hope that helped (-:

7 0

2 years ago

The base is 3 and the height is 2 what is the area of the triangle

Scorpion4ik [409]

Answer:

area = 3

Step-by-step explanation:

area of a triangle = 1/2 base x height

1/2 x 3 x 2 = 1/2 x 6 = 3

6 0

2 years ago

1. The US Mint has a specification that pennies have a mean weight of 2.5g. From a sample of 37 pennies, the mean weight is foun

Evgesh-ka [11]

Answer:

the pennies does not conform to the US mints specification

Step-by-step explanation:

z = (variate -mean)/ standard deviation

z= 2.5 - 2.4991 / 0.01648 = 0.0546

we are going to check the value of z in the normal distribution table, which is the table bounded by z.

checking for z= 0.0 under 55 gives 0.0219 (value gotten from the table of normal distribution)

we subtract the value of z from 0.5 (1- (0.5+0.0219)) = 0.4781 > 0.05claim

since 0.4781 > 0.05claim, therefore, the pennies does not conform to the US mints specification

the claim state a 5% significance level whereas the calculated significance level is 47.81%. therefore, the claim should be rejected

7 0

3 years ago