( I ) A log cabin has an interior volume of 200 m^3. (a) Find the mass of the air contained in the cabin at 20 degrees celsius and at 1 atm. (b) If we heated the cabin at 28 degrees celcius, what would be the new pressure , assuming the cabin is airtight? (c) If the cabin was not airtight, how much air would escape if the temperature was increased? Assume that the molar mass of air molecules is equal to 29 g/mol.

( II ) A railway track is laid at 15 degrees with 17 m long rails. What is the minimum space required between the ends of the rails if a maximum temperature of 33 degrees celcius is expected?

( III ) The central portion of the Pierre Laporte bridge is 667 m long. At each end of this steel structure is an expansion joint allowing a clearance of 21.9 cm. The average temperature in Quebec being 4 degrees celcius, what extreme temperatures can this construction withstand?

( IV ) A hot air balloon has a volume of 1009 m^3. The ambient air temperature is equal to 17 degrees Celsius and the pressure to 1 atm. What value must the temperature of the air in the balloon reach for it to manage to lift just 186 kg (including the mass of the balloon)? Assume that the "effective" molar mass of air molecules is equal to 29 g/mol.

( V ) A steel rod with a radius of 2.1 cm, the ends of which are fixed, is subjected to a tension force of modulus 19 kN at both ends. What is the stress if the temperature (a) drops 10 degrees celcius; (b) rises 10 degrees celcius? (Young's modulus of steel is 2 x 10^11 N/m2^2.)