Solving a Diatomic Ideal Gas Problem: Find Temp & Energy Transfer

[burgerkin]

Homework Statement

A cylindar w/ a moving piston holds 3.50 mol of a diatomic ideal gas. The initial vol. is Vi, and its temperature is Ti. Then the cylinder is set on a heat plate and additional weights are placed onto the piston as it moves up, and pressure is proportional to the volume and the final volume is 6Vi.

1, Find the final Temperature

2, find the energy transfer by heat

Homework Equations

pv =nRT

The Attempt at a Solution

I got the first part, the answer is Tf = 36 Ti

For second part, I thought it was straight forward, but the answer was wrong

I did :

Q=n Cv (Tf-Ti) = 3.5 x (5/2) R x 35 Ti =306.25 RTi

but the correct answer is 367.5 RTi

what did I do wrong?

Thanks!

 

[burgerkin]

please help. thanks!

 

[cjl]

You forgot to account for the work done by the gas as it expanded. You correctly accounted for the internal energy change, but some of the energy went into lifting the weights.

 

[burgerkin]

oh i see. I was confused about heat and Q.

So the energy transfer by heat means the energy that caused the increase in temperature and the energy that the gas expands--work done by gas.

So E =Q +W
E=nCv$$\Delta$$T

but how do I calculate Work? What kind of expansion is this. I see volume, pressure, temperature all change, so i do not know how to get work.

 

[ehild]

Read the problem: "pressure is proportional to the volume" How do you calculate the work of the gas?

ehild

 

[burgerkin]

W= -P(Vf-Vi) ?

i am not sure what does it imply" P is proportional to V..

 

[burgerkin]

I don't think I understand the physics of this well. sO THE presssure is the pressure of the gas? As it is heated up, it expands, then pressure should be decreasing, isn't it? But yet this is not a free expansion.

 

[ehild]

It is usually assumed that the pressure of the gas is balanced by the pressure of the external forces, here the atmospheric pressure and that of the weights put on the piston gradually. Work is

W=∫PdV from Vi to Vf and P=const*V.

ehild

 

[TROGLIO]

press is proportional to volume
so let's ay press = k x vol
now work done is dw = (integral) p x dv
pure math actually not much physics