A gas is confined in a $0\mathrm{.}47-$m$-$diameter cylinder by a piston, on which rests a weight. The mass of

the piston and weight together is $150$ kg$.$ The local accelera$>$on of gravity is $9\mathrm{.}813$ m s$-2$

$,$ and

atmospheric pressure is $101\mathrm{.}57$ kPa.

a$)$ What is the force in Newton exerted on the gas by the atmosphere, the piston, and the

weight, assuming no fric$>$on between the piston and cylinder?

b$)$ What is the pressure of the gas in kPa?

c$)$ If the gas in the cylinder is heated, it expands, pushing the piston and weight upward. If

the piston and weight are raised $0\mathrm{.}83$ m$,$ what is the work done by the gas in kJ$?$ What is

the change in poten$>$al energy of the piston and weight?