A vertical piston$/$cylinder device contains $0\mathrm{.}01lbm$ of gas. The gas has an initial volume of $0\mathrm{.}2f{t}^3.$ The piston, with a mass of $200lbm$ and cross$-$sectional area of $0\mathrm{.}1f{t}^2,$ is in equilibrium with the gas. The outside ambient pressure is $1$atm. The gas now undergoes a process in which the volume increases to $0\mathrm{.}3f{t}^3$ and the specific internal energy decreases by $10Bt\frac{u}{l}bm.$ Assume a quasiequilibrium process in which piston movement is slow with no acceleration. Friction between the piston and cylinder is negligible. Determine:

a$.$ Work $[$Btu$]$ during the process $($magnitude and direction$)$

b$.$ Heat transfer Btu during the process $($magnitude and direction$)$

Draw a VP digram as well