Question

The gas is in a cylinder with V = 4500 mL; t0 = 70 ℃; p1 = 2.4 atm. The cylinder is heated in an isobaric process until the volume is increased 3.4 times. Find the mass of the gas,density, substance quantity and final temperature as well as the mean square velocity. What work could be done in this process? How does the internal energy of the system change? Present: gas is nitrogen

Answer 1

Explanation:

When an ideal gas is compressed adiabatically \left(Q=0\right), work is done on it and its temperature increases; in an adiabatic expansion, the gas does work and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment. Nevertheless, because work is done on the mixture during the compression, its temperature does rise significantly. In fact, the temperature increases can be so large that the mixture can explode without the addition of a spark. Such explosions, since they are not timed, make a car run poorly—it usually “knocks.” Because ignition temperature rises with the octane of gasoline, one way to overcome this problem is to use a higher-octane gasoline.

Another interesting adiabatic process is the free expansion of a gas. (Figure) shows a gas confined by a membrane to one side of a two-compartment, thermally insulated container. When the membrane is punctured, gas rushes into the empty side of the container, thereby expanding freely. Because the gas expands “against a vacuum” \left(p=0\right), it does no work, and because the vessel is thermally insulated, the expansion is adiabatic. With Q=0 and W=0 in the first law, so for the free expansion.

The gas in the left chamber expands freely into the right chamber when the membrane is punctured.