Question

A container of gas at 2.7 atm pressure and 133 ∘C is compressed at constant temperature until the volume is halved. It is then further compressed at constant pressure until the volume is halved again.

a) What is the final pressure (atm)?
b) What is the final temperature (C)?

Answer 1

The final pressure of the gas after being compressed at constant temperature and then at constant pressure is 5.4 atm. The final temperature remains unchanged at 133 °C.

Step-by-step explanation:

The question involves finding the final pressure and final temperature of a gas after two consecutive processes: compression at constant temperature and then compression at constant pressure. The first part of the question looks at Boyle's Law, where the pressure and volume of a gas are inversely proportional at a constant temperature. The second part applies Charles's Law, where the volume and temperature are directly related at a constant pressure.

• a) Final pressure: Since the container is compressed at a constant temperature, the pressure of the gas will increase as the volume decreases. According to Boyle's Law, if the volume is halved, the pressure will double. So, after the first compression, the pressure is 2.7 atm * 2 = 5.4 atm. The gas is then further compressed at constant pressure, so the final pressure remains 5.4 atm.
• b) Final temperature: As the gas is compressed at constant pressure, the temperature will not change. Hence, the final temperature remains the same as the initial temperature, which is 133 °C.