A-level Physics (Advancing Physics)/Ideal Gases/Worked Solutions

'''1. I heat some argon from 250°K to 300°K. If the pressure of the gas at 250°K is 0.1 MPa, what is its pressure after heating?'''

The temperature has increased by 20%, so the pressure will also increase by 20% (using the pressure law). So, the new pressure is 0.1 MPa x 1.2 = 0.12 MPa.

2. The argon is in a 0.5m long cylindrical tank with radius 10 cm. What volume does it occupy?

$$V = \pi r^2 l = \pi \times 0.1^2 \times 0.5 = 0.016\mbox{ m}^3$$

'''3. The argon is then squeezed with a piston so that in only occupies 0.4m of the tank's length. What is its new pressure?'''

The volume occupied decreases by 20%, which is equivalent to multiplying by 0.8. So, by Boyle's Law, the pressure is multiplied by the reciprocal of 0.8 - 1.25. So, the pressure increases by 25% to 0.15 MPa.

4. What is its new temperature?

If we combine Charles' Law with the pressure law, we find that:

$$T \propto pV$$

Volume is multiplied by 0.8, but pressure is multiplied by 1.25, so there is no change in temperature - it remains at 300°K.

'''5. 25% of the argon is sucked out. What is its pressure now?'''

Using the amount law, if N decreases by 25%, the pressure must also decrease by 25% to 0.1125 MPa.