PC2352 Examples 3

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4.

A fridge is operating in a room at 20$^{{\rm o}}$ C and the interior temperature is 4$^{{\rm o}}$ C. The leakage of heat through the walls of the fridge is 30 W per degree Kelvin of temperature difference between the interior and the exterior. What is the minimum power required to run the fridge? How much will a real fridge cost to run per day?
Similar examples can be found here.

5.

(a)

For each of the processes (i), (ii) and (iv) of question 2 on examples 2, what is the entropy change of the system, and of the universe?

(b)

A 10kg lump of copper at $100^{\rm o}$C is cooled reversibly to $10^{\rm o}$C. Calculate the change in entropy of the block. What is the change in entropy of the universe as a result of the process?

(c)

A 10kg lump of copper at $100^{\rm o}$C is cooled irreversibly by dumping it in a lake at $10^{\rm o}$C. What is the change in entropy of the block? What is the change in entropy of the universe?

(The specific heat capacity of copper is 375Jkg$^{-1}$K$^{-1}$)

More worked examples of entropy changes are found here.

6.

(a)

At atmospheric pressure, lead melts at $601$K, its density decreasing from $1.101\times 10^{4}$kgm$^{-3}$ to $1.065\times 10^{4}$kgm$^{-3}$. The latent heat of fusion is 24.5kJkg$^{-1}$. Estimate the melting point at 100 atmospheres.

(b)

The melting point of ice falls with increasing pressure. Thus the pressure of the blade of an ice skate can cause ice to melt and lubricate the skate, allowing the skater to glide with very little friction. If the ice temperature is too low this cannot happen and it spoils the skating. Calculate a lowest temperature for good skating. You may assume that the effective area of contact between the blade and the ice is 5mm$^2$ and that the skater's mass is 60kg.

(The latent heat of fusion of ice is $3.35 \times 10^5$Jkg$^{-1}$ and the densities of ice and water near 0$^{\circ}$C are 0.9168gcm$^{-3}$ and 0.9999gcm$^{-3}$ respectively).

Can you think of any effects which you have ignored which may significantly change this estimate?

These problems use the Clausius-Clapeyron equation. Remember to refer all quantities (latent heat, volume change) to the same amount of material, and be careful in calculating the volume change from the density change.