- #1
jeebs
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Hi, i think I've got the first part of this question done but I am stuck with the rest, so i'll post the lot in case you think i have the first part wrong.
a) Derive and expression for the work done by an ideal gas when it expands isothermally at temperature T from a volume V1 to V2.
b) calculate the work done when T = 25 degrees C and V2 = 3V1.
c) calculate the magnitude and direction of the flow of heat during the above process.
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Here is my attempt. for the first part, i am imagining a gas expanding like burning petrol in a car engine, the gas is forcing the piston of area A a distance x along the cylinder:
a) work done dW = F.dx (work = force x displacement).
F = pA (force = pressure x area). change in volume dV = A.dx
therefore dW = pA.dx = p.dV, so W = ∫ p.dV
and since pV = nRT we can write that W = nRT∫(1/V).dV = (nRT).ln(V)
so, W = (nRT).ln(V2) - (nRT).ln(V1) = nRT.ln(V2/V1).
b) to calculate the work done, i plugged the numbers into the equation (the ln(V2/V1) part becomes ln(3) ) but i do not know the number of moles, therefore i am stuck with the n term.
the closest i can get to an answer is 2720.58 Joules per mole.
can anyone help me out here?
EDIT: apologies, it turns out that my problem sheet had information missing from it. there was one mole of gas present, n=1.
so part b) is completed.c) i have no idea how to do this.
does anyone know what i have to do? i am very grateful for any help.
thanks.
a) Derive and expression for the work done by an ideal gas when it expands isothermally at temperature T from a volume V1 to V2.
b) calculate the work done when T = 25 degrees C and V2 = 3V1.
c) calculate the magnitude and direction of the flow of heat during the above process.
----------------------------------------------------------------------------------------------------------------------------
Here is my attempt. for the first part, i am imagining a gas expanding like burning petrol in a car engine, the gas is forcing the piston of area A a distance x along the cylinder:
a) work done dW = F.dx (work = force x displacement).
F = pA (force = pressure x area). change in volume dV = A.dx
therefore dW = pA.dx = p.dV, so W = ∫ p.dV
and since pV = nRT we can write that W = nRT∫(1/V).dV = (nRT).ln(V)
so, W = (nRT).ln(V2) - (nRT).ln(V1) = nRT.ln(V2/V1).
b) to calculate the work done, i plugged the numbers into the equation (the ln(V2/V1) part becomes ln(3) ) but i do not know the number of moles, therefore i am stuck with the n term.
the closest i can get to an answer is 2720.58 Joules per mole.
can anyone help me out here?
EDIT: apologies, it turns out that my problem sheet had information missing from it. there was one mole of gas present, n=1.
so part b) is completed.c) i have no idea how to do this.
does anyone know what i have to do? i am very grateful for any help.
thanks.
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