Answer
(a) $N·m$
(b) $k = 20 N·m$
(c) Refer to the table in the picture below
(d) Refer to the graph in the picture below
Work Step by Step
(a) $k = PV$
Unit of $P = N/m^2$ and for $V = m^3$
$k = \frac{N}{m^2}\times m^3$
$\therefore k = N.m$
(b) $P = 20,000N/m^2$, $V = 0.001m^3$
$k = 20000 \times 0.001$
$k = 20N.m$
(c) $k = 20N.m$
$V = 0.25l \times 0.001m^3 = 0.00025m^3$
$P = \frac{k}{V}$
$P = \frac{20}{0.00025}$
$\therefore P = 80,000N/m^2 = 80 \times 10^3N/m^2$
$V = 0.5l \times 0.001m^3 = 0.0005m^3$
$P = \frac{20}{0.0005}$
$\therefore P = 40,000N/m^2 = 40 \times 10^3N/m^2$
$V = 1l \times 0.001m^3 = 0.001m^3$
$P = \frac{20}{0.001}$
$\therefore P = 20,000N/m^2 = 20 \times 10^3N/m^2$
$V = 1.5l \times 0.001m^3 = 0.0015m^3$
$P = \frac{20}{0.0015}$
$\therefore P = 13,333.33N/m^2 = 13.3 \times 10^3N/m^2$
$V = 2l \times 0.001m^3 = 0.002m^3$
$P = \frac{20}{0.002}$
$\therefore P = 10,000N/m^2 = 10 \times 10^3N/m^2$
(d) Refer to the graph above
