Nitrogen at $900\ \mathrm{kPa}$ and $300^{\circ} \mathrm{C}$ is expanded adiabatically in a closed system to $100\ \mathrm{kPa}$. Find the minimum nitrogen temperature after the expansion.

Explain the difference between the entropies of air at $15 \mathrm{psia}$ and $70^{\circ} \mathrm{F}$ and air at $40 \mathrm{psia}$ and $250^{\circ} \mathrm{F}$ per unit mass basis.

Air is expanded from 2000 kPa and $500^{\circ} \mathrm{C}$ to 100 kPa and $50^{\circ} \mathrm{C}.$ Assuming constant specific heats, determine the change in the specific entropy of air.

Which of the two gases—helium or nitrogen— experiences the greatest entropy change as its state is changed from 2000 kPa and $427^{\circ} \mathrm{C}$ to 200 kPa and $27^{\circ} \mathrm{C} ?$

Prove that the two relations for entropy change of ideal gases under the constant-specific-heat assumption are equivalent.

An ideal gas undergoes a process between two specified temperatures, first at constant pressure and then at constant volume. For which case will the ideal gas experience a larger entropy change? Explain.

Can the entropy of an ideal gas change during an isothermal process?

Some properties of ideal gases such as internal energy and enthalpy vary with temperature only. Is this also the case for entropy?

An adiabatic pump is to be used to compress saturated liquid water at $10\ \mathrm{kPa}$ to pressure to $15\ \mathrm{MPa}$ in a reversible manner. Find the work input using $(a)$ entropy data from the compressed liquid table, (b) inlet specific volume and pressure values, and $(c)$ average specific volume and pressure values. Also, find the errors involved in parts $(b)$ and $(c)$.

The entropy of a hot baked potato decreases as it cools. Is this a violation of the increase of entropy principle? Explain.

The breaking strengths of $n = 20$ bundles of wool fibers have a sample mean $\bar{x} = 436.5$ and a sample standard deviation $s_x = 11.90$. In addition, the breaking strengths of $m = 25$ bundles of synthetic fibers have a sample mean $\bar{y} = 452.8$ and a sample standard deviation $s_y = 4.61$. Answer the following questions without assuming that the two population variances are equal. (a) Does a one-sided hypothesis test with size $\alpha = 0.01$ accept or reject the null hypothesis that the synthetic fiber bundles have an average breaking strength no larger than the wool fiber bundles? (b) What is a one-sided $99\%$ confidence interval that provides an $\textit{upper bound}$ on $\mu_A -\mu_B$, where $\mu_A$ i is the average breaking strength of wool fiber bundles and $\mu_B$ is the average breaking strength of synthetic fiber bundles? (c) Is there enough evidence to conclude that the average breaking strength of synthetic fiber bundles is larger than the average breaking strength of wool fiber bundles?

A 50-kg iron block and a 20-kg copper block, both initially at $80^{\circ} \mathrm{C}$, are dropped into a large lake at $15^{\circ} \mathrm{C}$. Thermal equilibrium is established after a while as a result of heat transfer between the blocks and the lake water. Find the total entropy change for this process.

A 30-kg aluminum block initially at $140^{\circ} \mathrm{C}$ is brought into contact with a 40-kg block of iron at $60^{\circ} \mathrm{C}$ in an insulated enclosure. Determine the final equilibrium temperature and the total entropy change for this process.

A 25-kg iron block initially at $350^{\circ} \mathrm{C}$ is quenched in an insulated tank that contains 100 kg of water at $18^{\circ} \mathrm{C}.$ Assuming the water that vaporizes during the process condenses back in the tank, determine the total entropy change during this process.