15.6 Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy

Equal masses of steam (100 degrees C) and ice (0 degrees C) are placed in contact with each other in an otherwise insulated container. They both end up as liquid water at a common temperature. The steam ___ entropy and ___ order, while the ice ___ entropy and ___ order.

1. gained, gained, lost, lost
2. gained, lost, lost, gained
3. lost, gained, gained, lost
4. lost, lost, gained, gained

(a) On a winter day, a certain house loses $5 . \text{00} \times \text{10}^{8} \text{ J}$ of heat to the outside (about 500,000 Btu). What is the total change in entropy due to this heat transfer alone, assuming an average indoor temperature of $\text{21}.\text{0}º\text{ C}$ and an average outdoor temperature of $5.00º C$? (b) This large change in entropy implies a large amount of energy has become unavailable to do work. Where do we find more energy when such energy is lost to…

A hot rock ejected from a volcano’s lava fountain cools from $\text{1100}º\text{ C}$ to $\text{40}.\text{0}º\text{ C}$, and its entropy decreases by 950 J/K. How much heat transfer occurs from the rock?

The Sun radiates energy at the rate of $3 . \text{80} \times \text{10}^{\text{26}} \text{ W}$ from its $\text{5500}º\text{ C}$ surface into dark empty space (a negligible fraction radiates onto Earth and the other planets). The effective temperature of deep space is $- \text{270}º\text{ C}$. (a) What is the increase in entropy in one day due to this heat transfer? (b) How much work is made unavailable?

What is the decrease in entropy of 25.0 g of water that condenses on a bathroom mirror at a temperature of $\text{35}.\text{0}º\text{ C}$, assuming no change in temperature and given the latent heat of vaporization to be 2450 kJ/kg?

A large electrical power station generates 1000 MW of electricity with an efficiency of 35.0%. (a) Calculate the heat transfer to the power station, $Q_{\text{h}}$, in one day. (b) How much heat transfer $Q_{\text{c}}$ occurs to the environment in one day? (c) If the heat transfer in the cooling towers is from $\text{35}.\text{0}º\text{ C}$ water into the local air mass, which increases in temperature from $\text{18}.\text{0}º\text{ C}$ to $\text{20}.\text{0}º\text{ C}$, what is the total increase in entropy…