# How far does the piston move

## Homework Statement

The ﬁgure shows a 50 kg lead cylindrical piston that ﬂoats on 0.68 mol of compressed air at 30°C. How far does the piston move if the temperature is increased to 300°C? (the base of the beaker is 10cm.

A)130 cm B)1300 cm C)120 cm D)250 cm

?

## The Attempt at a Solution

no clue

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Think "Energy Balance"

Can you relate the internal energy change due to $\Delta T$ to the work needed to raise the piston?

is this a proper equation U= W+Q?

Yes. That is the "Energy Balance" for a thermodynamic system.

Now, what do each of the three terms represent?

internal energy= work + heat, and since temperature increases, internal energy increases also?

Yes. Internal energy in a direct measure of the temperature change, you should have read somewhere that:

$\Delta U=mc\Delta T$ (or something similar depending whether it is a per mass basis or molecular basis) and that $W=\int p\, dV$

ok so i have mass and change of T, how do i find C, also what do i do once i have change of U

Generally, values of specific heat are tabulated in your text.

also what do i do once i have change of U
You tell me. What about your Work term? Your heat term Q is zero (I am assuming you can see why).

What is the work here? Can you find distance the piston travels using the Work term?

Hint: You were given area.