Question

3. Suppose that a gas originally at standard temperature and pressure undergoes a change in which its pressure is quadrupled while its temperature is cut in half. What change in volume does the gas experience during this process?
(Standard temperature and pressure are 273.15 K and 100 000 Pa)

Answer 1

Answer:

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Answer 2

Given: A gas originally at standard temperature and pressure undergoes a change in which its temperature is quadrupled while its temperature is cut in half.

To find: Change in volume the gas experiences

Explanation: Combining all the relationships given between pressure and temperature by Gay- Lussac's Law, volume and temperature by Charles law and pressure and volume by Boyle's law, we get the formula:

P1V1/T1 = P2V2/T2

The pressure is quadrupled, that means:

P2 = 4 P1

The temperature is cut in half, that means:

T2 = T1/2

Let volume before and after the change be V1 and V2 respectively.

Using these:

P1 V1 / T1 = 4 P1 V2 / (T1/2)

=> P1 V1 / T1 = 8 P1 V2 /T1

=> V1 = 8 V2

=> V2 = V1 / 8

Therefore, the volume decreases by 8 times the previous volume during this process.