A gas, while expanding under isobaric conditions, does 660 J of work. The pressure of the gas is 1.40 x 105 Pa, and its initial volume is 1.70 x 10-3 m3. What is the final volume of the gas?
Would I multiply the two values?
W = p*dV = p(Vf - Vi)--for isbaric p is constant.
Plug in values of W,p and Vi to find Vf
So I set this up as 660=1.40e^5(1.70e^-3 - Vf)
Then to solve for Vf I multiplied 1.70e^-3 and 1.40e^5 and then divided by 660. Did I do this correctly?
Yes, you set up the equation correctly. To solve for the final volume, you would divide both sides of the equation by the pressure (p) and then add the initial volume (Vi) to both sides. Here's the step-by-step solution:
1. Start with the equation:
W = p * (Vf - Vi)
2. Plug in the given values:
W = 660 J
p = 1.40 x 10^5 Pa
Vi = 1.70 x 10^-3 m^3
3. Rearrange the equation:
W = p * (Vf - Vi)
Divide both sides by p:
W / p = Vf - Vi
4. Substitute the given values:
660 J / (1.40 x 10^5 Pa) = Vf - (1.70 x 10^-3 m^3)
5. Simplify the left side of the equation:
4.714 x 10^-3 m^3 = Vf - 1.70 x 10^-3 m^3
6. Add 1.70 x 10^-3 m^3 to both sides:
4.714 x 10^-3 m^3 + 1.70 x 10^-3 m^3 = Vf - 1.70 x 10^-3 m^3 + 1.70 x 10^-3 m^3
7. Simplify:
6.414 x 10^-3 m^3 = Vf
Therefore, the final volume of the gas is 6.414 x 10^-3 m^3.
Yes, you set up the equation correctly. To solve for Vf, you can rearrange the equation as follows:
660 = (1.40 x 10^5)(1.70 x 10^-3 - Vf)
Next, you can divide both sides of the equation by (1.40 x 10^5) to solve for (1.70 x 10^-3 - Vf):
660 / (1.40 x 10^5) = 1.70 x 10^-3 - Vf
Now, subtract 1.70 x 10^-3 from both sides of the equation:
Vf = 1.70 x 10^-3 - (660 / (1.40 x 10^5))
To calculate the final volume (Vf), you need to substitute the given values into the equation:
Vf = 1.70 x 10^-3 - (660 / (1.40 x 10^5))
After performing the calculation, you will find the final volume of the gas.