A material with perfect crystallinity was cooled to near $0K.$ Can the entropy of the material be estimated?

a$.$ Yes, the entropy of a single crystal material approaches $0$ as it approaches $0K.$

b$.$ No$,$ entropy of any material depends on their chemistry and cannot be estimated.

c$.$ Yes, the entropy of a material does not vary with temperature, so entropy is constant.

d$.$ No$,$ the entropy of materials does not show any predictable trend.

Which of the following scenario can Helmholtz free energy be used to predict spontaneity?

a$.$ A chemical reaction between two dissolved metal salts in an open beaker held constant at room temperature.

b$.$ A physical process happening on the leaves of a tree turning water into water vapor.

c$.$ A chemical reaction happening in a tightly sealed water bottle turning sugar into alcohol.

d$.$ None of the above.

A cup of water is suspended in a larger bowl of water. The outer bowl of water is heated to boiling. What would happen to the inner cup of water?

a$.$ The inner cup of water would reach $100C$ and it would boil vigorously.

b$.$ The inner cup of water would reach a temperature that is just below $100C.$

c$.$ The inner cup of water would reach a temperature that is just below $100C,$ and the water would evaporate quickly.

d$.$ The inner cup of water would reach $100C,$ but it does not boil.

When $100mL$ of sample A and $50mL$ of sample $B$ are carefully mixed together, the combined homogeneous solution measures $140mL.$ If no chemical reactions occurred, which of the following must be true.

a$.$ Dissimilar molecules have stronger intermolecular interactions than those found in the pure samples.

b$.$ Dissimilar molecules have weaker intermolecular interactions than those found in the pure samples.

c$.$ Dissimilar molecules do not interact with each other.

d$.$ This phenomenon disobeys the conservation of mass, so some of the material must have been lost during the transferring process. There is no other plausible explanation.

A new refrigerator is being showcased at an exhibition. This refrigerator uses new materials to achieve reverse Carnot cycle based cooling from $25C$ to $4C.$ The presenter argued that they achieved a maximum COP of $110\%,$ which seem impressive. However, this number doesn't seem to be correctly presented. Based on what you know about Carnot cycles, which of the following is the most suitable explanation?

a$.$ The optimal COP is over $10,$ which would indicate the exhibited refrigerator is not efficient.

b$.$ The maximum COP is $100\%,$ which would make the exhibited value incorrect.

c$.$ The optimal COP is $160\%,$ so the exhibited value is competitive with the ideal performance of $70\%$ efficiency for most Carnot cycles.

d$.$ The exhibitors are correct, no correction needed.