Calculating Heat Transfer in a Water Bath with a Changing Volume and Temperature

[Physgeek64]

Homework Statement

A cylinder is fitted with a piston and is in thermal contact with a heat bath at 273K. Initially the volume in the cylinder is filled with 10kg of pure H2O and about half of this is liquid and the other half is solid. The piston is lowered so as to reduce the volume by 2 × 10−5 m3. What is the sign and magnitude of the heat transfer to the bath?

Homework Equations

The Attempt at a Solution

$\frac{dp}{dT}=\frac{L}{T\Delta V}$
$p_2-p_1= \frac{L}{\Delta V} ln{\frac{T_2}{T_1}}$
but $T_1=T_2$ hence $p_1=p_2=constant$
$dQ=dU+pdV=C_VdT+pdV=pdV$
$\Delta Q=p\Delta V$

I feel this is probably all wrong, but i can't see how else to do it- any help would be very much appreciated.

 

[mjc123]

What are the densities of ice and water at 273K? How much ice must be converted to water, or vice versa, to reduce the total volume by 2 x 10^-5 m³?

 

[Physgeek64]

What are the densities of ice and water at 273K? How much ice must be converted to water, or vice versa, to reduce the total volume by 2 x 10^-5 m³?

$V=\frac{M}{\rho}$
$\Delta V= \delta \big{(} \frac{1}{\rho_l} + \frac{1}{\rho_s} \big{)}$
where $\delta$ is the mass that is converted from solid to liquid.
$\delta= 9.58 \times 10^{-3}$

Can we then use $lM=T\Delta S = \Delta Q$
$\Delta Q = l \delta = 3191.25 J$ ?

where l is the specific latent heat of fusion of ice

 

[mjc123]

ΔV=δ(1ρl+1ρs)ΔV=δ(1ρl+1ρs)\Delta V= \delta \big{(} \frac{1}{\rho_l} + \frac{1}{\rho_s} \big{)}

(Why does it always look wrong in quotes?)
Why the plus sign? You want the difference in volume between liquid and solid.

 

[Physgeek64]

(Why does it always look wrong in quotes?)
Why the plus sign? You want the difference in volume between liquid and solid.

Ahh yes! So with the minus sign, does this look right?

Thanks

 

[DrClaude]

(Why does it always look wrong in quotes?)

Selecting text to quote appears to translate away from the underlying LaTeX. To get it to display properly, you have to use the Reply "button" on the lower right-hand side of the post. That will quote the entire post, but you can trim it down if you just want to quote a part.

 

[mjc123]

Ahh yes! So with the minus sign, does this look right?

Should be. Be careful with the sign of Q.