Can you help me with this? If you can, do it as detail as you can. If not, you can just give me the answer, i'll try to figure how you did it :|
A sample of gas in a cylinder of volume 3.96 L at 327 K and 3.28 atm expands to 7.34 L by two different pathways. Path A is an isothermal, reversible expansion. Calculate the work for Path A.
Answer in units of J.
To calculate the work for Path A, we need to use the formula for work in an isothermal reversible expansion:
Work (W) = -P external * ΔV
Where:
- P external is the external pressure
- ΔV is the change in volume
In this case, since it's an isothermal expansion, the temperature remains constant at 327 K.
Let's break down the calculation step by step:
Step 1: Calculate the change in volume (ΔV)
ΔV = V final - V initial
ΔV = 7.34 L - 3.96 L
ΔV = 3.38 L
Step 2: Identify the external pressure (P external)
In this case, the external pressure is given as 3.28 atm.
Step 3: Convert the external pressure to SI units (atm to Pa)
1 atm = 101325 Pa
So, P external = 3.28 atm * 101325 Pa/atm
P external = 332914 Pa
Step 4: Calculate the work (W)
W = -P external * ΔV
W = -(332914 Pa) * (3.38 L)
Now, let's do the calculation:
W = -(332914 Pa) * (3.38 L)
W = -1,123,962.932 Pa * L
Since the unit of work is Joules (J), we need to convert the given unit of Pa * L to J. To do that, we need to use the conversion factor:
1 J = 1 Pa * m^3
Now, we need to convert liters (L) to cubic meters (m^3) first:
1 L = 0.001 m^3
So, 3.38 L = 3.38 * 0.001 m^3
3.38 L = 0.00338 m^3
Substituting the values:
W = -1,123,962.932 Pa * 0.00338 m^3
W = -3805.04 J
Since work is a scalar quantity, we drop the negative sign in the final answer.
Therefore, the work for Path A is approximately 3805 J.