- #1
CAF123
Gold Member
- 2,948
- 88
Homework Statement
Consider a frictionless piston inside a cylinder, both with a cross sectional area A.
1) By considering the work done by the gas on the piston and the work dW required to move the piston a distance dx, show that the work done by the gas is dW = -pdV.
2) 1 L of an ideal gas is at a pressure of 5 atm. If it then expands at constant temperature against a frictionless piston until It's pressure falls back to atmospheric pressure, calculate I) the final volume of gas, 2) the work done on (or is it by?) the gas?
The Attempt at a Solution
1) The force of the gas on the piston is PA. Then W = Fdx = PA dx = PdV. This is straightforward but I have a positive work. Is there a mistake in the question? dx and F are in same direction so by definition, this is positive work.
2) I) 5L ii) So dV = 4 L . The work done will be by the gas since it is the gas that is expanding and the piston does not act to compress. I don't think I can use the above relation because the pressure is not constant. I will try an integral. Is this the right way to proceed?
EDIT: The integral I have is $$W = nRT\int_{V_o}^{V_f} \frac{dV}{V} = nRT[ln(V_f) - ln(V_o)] = nRT ln \left(\frac{V_f}{V_o}\right)$$ I would have then an answer of ##nRT ln(5)##, since I don't know n or T and R is a constant.
Last edited: