<h2>
Answer:</h2>
(a) V =
(b) (i) the value of when P = 50kPa is - 0.00332
(ii) the meaning of the derivative is the rate of change of volume with pressure.
(iii) and the units are
<h2>
Explanation:</h2>
Boyle's law states that at constant temperature;
P ∝ 1 / V
=> P = k / V
=> PV = k -------------------------(i)
Where;
P = pressure
V = volume
k = constant of proportionality
According to the question;
When;
V = 0.106m³, P = 50kPa
Substitute these values into equation (i) as follows;
50 x 0.106 = k
Solve for k;
k = 5.3 kPa m³
(a) To write V as a function of P, substitute the value of k into equation (i) as follows;
PV = k
PV = 8.3
Make V subject of the formula in the above equation as follows;
V = 8.3/P
=> V = -------------------(ii)
(b) Find the derivative of equation (ii) with respect to V to get dV/dP as follows;
V =
V = 8.3P⁻¹
= -8.3P⁻²
=
Now substitute P = 50kPa into the equation as follows;
= [] ----- Write and evaluate the units alongside
= []
= - 0.00332 []
Therefore,
(i) the value of when P = 50kPa is - 0.00332
(ii) the meaning of the derivative is the rate of change of volume with pressure.
(iii) and the units are