The pressure P of a gas is related to its volume V by the formula P=k/V where k is a constant. A quantity of gas with an initial volume of 1 cubic meter and a pressure of 2.5 newtons per square meter expands to a volume of 16 cubic meters. Find the work done by the gas.

Please help! I just don't know what to put inside the integral!

To find the work done by the gas, we need to use the formula for work in terms of pressure and volume.

The formula for work is given by: Work = Force × Distance

In this case, the force is the pressure (P) exerted by the gas and the distance is the change in volume (ΔV) of the gas.

Given that the initial volume is 1 cubic meter and the final volume is 16 cubic meters, we can calculate the change in volume as follows:

ΔV = Final volume - Initial volume
= 16 m^3 - 1 m^3
= 15 m^3

Now, we need to find the value of the constant k to calculate the pressure at the initial volume.

Given the formula for pressure: P = k/V

We can rearrange the formula to solve for k:

k = P × V
= 2.5 N/m^2 × 1 m^3
= 2.5 N

Now, we can calculate the pressure at the final volume using the same formula:

P_final = k/V_final
= 2.5 N / 16 m^3
= 0.15625 N/m^2

To calculate the work done by the gas, we need to multiply the pressure at the initial volume by the change in volume:

Work = P_initial × ΔV
= 2.5 N/m^2 × 15 m^3
= 37.5 N

Therefore, the work done by the gas is 37.5 Newtons.