Question

The force required to compress the gas in a gas spring a distance x is given by $F = \frac{Constant}{x^k}$ where the constant is determined by the geometry of this device and k is determined by the gas used in the device. One such device has a constant of 200 lbf·in1.4 and k = 1.4. Determine the work, in Btu, required to compress this device from 2 in to 7 in.

Answer 1

Answer:

$W=1.155\times 10^{-2}\ btu$

Explanation:

Given relation:

Force, $F=\frac{c}{x^k}$

where:

$c=$ constant

$x=$ displacement

Constant of the given device, $c=200\ lbf.in^{1.4}$

initial position of piston, $x_i=2\ in$

final position of piston, $x_i=7\ in$

so the net displacement:

$\Delta x = x_f-x_i$

$\Delta x=7-2$

$\Delta x=5\ in$

Substituting the values in the given relation:

$F=\frac{200}{5^{1.4}}$

$F=21.012\ lbf$

Now the work done :

$W=F.\Delta x$

$W=21.012\times 5$

$W=105.061\ lbf.in$

• ∵$1\ lbf.in=11\times 10^{-5}\ btu$

So,

$W=1.155\times 10^{-2}\ btu$