Task $3$:

A$.$ Under what conditions is the ideal$-$gas assumption suitable for real gases?

B$.$ What is the difference between $R$ and $R_u?$ How are these two related?

C$.$ Propane and methane are commonly used for heating in winter, and the leakage of these fuels, even for short periods, poses a fire danger for homes. Which gas leakage do you think poses a greater risk for fire? Explain.

D$.$ A rigid tank $($figure $1)$ whose volume is unknown is divided into two parts by a partition. One side of the tank contains an ideal gas at $927C.$ The other side is evacuated and has a volume twice the size of the part containing the gas. The partition is now removed, and the gas expands to fill the entire tank. Heat is now applied to the gas until the pressure equals the initial pressure. Determine the final temperature of the gas.