QUESTION $2$

$($PO$1,$ CO$1,$ C$2)$

$1$ kg of ideal gas, initially at $100$ kPa and $300$ K contained in a piston$-$cylinder device as shown in Figure $1.$ A linear spring is attached to the piston and initially at rest. When heat is supplied to the system, the gas expands and causes the piston to hit the stops. The stops are at a distance of $10$ cm from the initial piston. The heating continues until the final pressure reads $500$ kPa

Figure

CONFIDENTIAL

a$)$ Calculate the work done by the gas against the spring, in kJ

b$)$ Determine the pressure of the gas when the piston first hits the stops, in kPa

c$)$ If the final temperature is $475$ K and assuming a constant specific heat of the gas is $\backslash (\backslash$mathrm$\{$C$\}\_\{\backslash$mathrm$\{$v$\}\}=0\mathrm{.}72\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}.\backslash$mathrm$\{$K$\}\backslash ),$ calculate the total heat transferred to the gas, in kJ

d$)$ Sketch the whole process on a P$-$V diagram. Label the states and the pressures clearly