Answer:
The slope is 2 and the y-intercept is -6
Step-by-step explanation:
we know that
The equation of the line in slope intercept form is equal to
where
m is unit rate or the slope of the linear equation
b is the y-intercept or initial value (value of y when the value of x is equal to zero)
In this problem we have
therefore
the slope is equal to
and
<u><em>Verify</em></u>
For x=0
---> is ok
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:
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
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