Hi!could anyone help me please, Thank.
Gas in a container is at a pressure of 1.3 atm and a volume of 1.0 m3.
(a) What is the work done on the gas if it expands at constant pressure to twice its initial volume?
(b) What is the work done on the gas if it is compressed at constant pressure to one-quarter its initial volume?
Sure! I can help you with that. To find the work done on the gas in both situations, we can use the formula:
Work (W) = P * ΔV
Where:
- Work (W) is the work done on the gas
- P is the pressure
- ΔV is the change in volume
(a) What is the work done on the gas if it expands at constant pressure to twice its initial volume?
To find the work done on the gas when it expands at constant pressure to twice its initial volume, we need to calculate the change in volume (ΔV). The initial volume is 1.0 m^3, and the final volume is twice the initial volume, which is 2 * 1.0 m^3 = 2.0 m^3.
Now, we can substitute the values into the formula:
Work (W) = P * ΔV
= 1.3 atm * (2.0 m^3 - 1.0 m^3)
= 1.3 atm * 1.0 m^3
= 1.3 atm * m^3
So, the work done on the gas when it expands at constant pressure to twice its initial volume is 1.3 atm * m^3.
(b) What is the work done on the gas if it is compressed at constant pressure to one-quarter its initial volume?
To find the work done on the gas when it is compressed at constant pressure to one-quarter its initial volume, we again need to calculate the change in volume (ΔV). The initial volume is 1.0 m^3, and the final volume is one-fourth of the initial volume, which is 1.0 m^3 / 4 = 0.25 m^3.
Now, we can substitute the values into the formula:
Work (W) = P * ΔV
= 1.3 atm * (0.25 m^3 - 1.0 m^3)
= 1.3 atm * (-0.75 m^3)
= -0.975 atm * m^3
Note that the work done on the gas is negative because the gas is being compressed, which means work is being done on the gas.
So, the work done on the gas when it is compressed at constant pressure to one-quarter its initial volume is -0.975 atm * m^3.
I hope this helps! Let me know if you have any further questions.