A box contains N identical gas molecules equally divided between its two halves. For N = 50, what is the percentage of the time the system spends in the central configuration?

A box contains N identical gas molecules equally divided between its two halves. For N = 50, what is the multiplicity W of the central configuration?

An ice-cream maker is kept cold by a reverse Carnot engine that removes 28.0 kJ as heat per cycle, with coefficient of performance 6.90. Per cycle, what are (a) the energy delivered as heat to the room and (b) the work done?

Show that for N molecules in a box, the number of possible microstates is $2^N$ when microstates are defined by whether a given molecule is in the left half of the box or the right half.

A Statistical View of Entropy

Construct a table for eight molecules.

The engine is then made to work in reverse to function as a Carnot refrigerator between those same two reservoirs. During each cycle, how much work is required to remove 1200 J as heat from the low-temperature reservoir?

A Carnot engine works between temperatures $T_1$ and $T_2$. It drives a Carnot refrigerator that works between temperatures $T_3$ and $T_4$. Find the ratio $Q_3 / Q_1$ in terms of $T_1, T_2, T_3$, and $T_4$.

An insulated Thermos contains 150 g of water at

$$80.0 ^ { \circ } \mathrm { C }$$

. You put in a 12.0 g ice cube at

$$0 ^ { \circ } \mathrm { C }$$

to form a system of ice + original water. (a) What is the equilibrium temperature of the system? What are the entropy changes of the water that was originally the ice cube (b) as it melts and (c) as it warms to the equilibrium temperature? (d) What is the entropy change of the original water as it cools to the equilibrium temperature? (e) What is the net entropy change of the ice + original water system as it reaches the equilibrium temperature?

During each cycle, a Carnot engine absorbs 750 J as heat from a high-temperature reservoir at 360 K, with the low-temperature reservoir at 280 K. How much work is done per cycle?

A gas is to be expanded from initial state i to final state f along either path 1 or path 2 on a p-V diagram. Path 1 consists of three steps: an isothermal expansion (work is 23 J in magnitude), an adiabatic expansion (work is 35 J in magnitude), and another isothermal expansion (work is 16 J in magnitude). Path 2 consists of two steps: a pressure reduction at constant volume and an expansion at constant pressure. What is the change in the internal energy of the gas along path 2?

Suppose $21.0 \mathrm{~g}$ of oxygen $\left(\mathrm{O}_2\right)$ gas is heated at constant atmospheric pressure from $25.0^{\circ} \mathrm{C}$ to $125^{\circ} \mathrm{C}$. How much energy is transferred to the oxygen as heat?

The temperature of 2.5 mol of a monatomic ideal gas is 350 K. The internal energy of this gas is doubled by the addition of heat. How much heat is needed when it is added at (a) constant volume and (b) constant pressure?

The temperature of 3.00 mol of an ideal diatomic gas is increased by 40.0 C$^\circ$ without the pressure of the gas changing. The molecules in the gas rotate but do not oscillate. How much energy is transferred to the gas as heat?

Chlorine gas is a diatomic molecule, $Cl_2$. There are 6.00 mol of chlorine atoms in a sample of chlorine gas. How many moles of chlorine gas molecules is this?