A block of copper at a temperature of $50^{\circ} \mathrm{C}$ is placed in contact with a block of aluminum at a temperature of $45^{\circ} \mathrm{C}$ in an insulated container. As a result of a transfer of 2500 J of energy from the copper to the aluminum, the final equilibrium temperature of the two blocks is $48^{\circ} \mathrm{C}.$ What is the approximate change in the entropy of the aluminum block?

Calculate the total rotational kinetic energy of all the mole- cules in $1$ mole of air at $25.0\degree\mathrm{C}$.

Adam Smith is important because ___.

A he wrote a book about communism

B his ideas form the basis of modern economics

C he was interested in becoming rich and famous

D he thought governments should make decisions for business

Find an expression for the change in entropy when two blocks of the same substance and of equal mass, one at the temperature $T_{h}$ the other at $T_{e},$ are brought into thermal contact and allowed to reach equilibrium. Evaluate the change in entropy for two blocks of copper, each of mass 500 g, with $C_{pm}=24.4\ \mathrm{JK}^{-1}\ \mathrm{mol}^{-1},$ taking $T_{\mathrm{h}}=500 \mathrm{K}$ and $T_{e}=250 \mathrm{K}.$

Complete the following sentences with vocabulary terms. Proteins are made from _______ that are joined by _______.

Find the column-row factorization and column-row expansion of the matrix.

$$\left[\begin{array}{rrrr}{2} & {-4} & {2} & {6} \\ {1} & {1} & {-4} & {-2} \\ {3} & {-9} & {8} & {14} \\ {0} & {6} & {-10} & {-10}\end{array}\right]$$

.

In a metric space M, if subsets satisfy $A \subseteq S \subseteq \overline{A}$, where $\overline{A}$ is the closure of A, the A is said to be dense in S. For example, the set Q of rational numbers is dense in R. A is dense in S and if S is dense in T, prove that A is dense in T.

Use your book or dictionary to define each term. Antibiotic _____.

Steam at $320^\circ C$ flows in a stainless steel pipe $(k = 15 W/m \cdot K)$ whose inner and outer diameters are 5 cm and 5.5 cm, respectively. The pipe is covered with 3-cm-thick glass wool insulation $(k = 0.038 W/m \cdot K).$ Heat is lost to the surroundings at $5^\circ C$ by natural convection and radiation, with a combined natural convection and radiation heat transfer coefficient of $15 W/m^2 \cdot K.$ Taking the heat transfer coefficient inside the pipe to be $80 W/m^2K,$ determine the rate of heat loss from the steam per unit length of the pipe. Also determine the temperature drops across the pipe shell and the insulation.

A real engine has an efficiency of $33\%$. The engine has a work output of $24~J$ per cycle.

(a) How much heat energy is extracted from the high-temper- ature reservoir per cycle? $(A)$ $8~J$ $(B)$ $16~J$ $(C)$ $48~J$ $(D)$ $72~J$ $(E)$ The question can be answered only if the engine is a Carnot engine.

(b) How much heat energy is discharged into the low-temper- ature reservoir per cycle? $(A)$ $8~J$ $(B)$ $16~J$ $(C)$ $48~J$ $(D)$ $72~J$ $(E)$ The question can be answered only if the engine is a Carnot engine.

(c) For this engine $T_L=27\degree C.$ What can be concluded about

$$T_H?$$

$(A)$ $T_H=450\degree C$. $(B)$ $T_H=177\degree C$. $(C)$ $T_H>177\degree C$. $(D)$ $T_H<177\degree C$. $(E)$ $177\degree C<T_H<450\degree C$.

Suppose that

$$x=\begin{bmatrix} -3,&0,&0,&2,&5,&8 \end{bmatrix}$$

and

$$y=\begin{bmatrix} -5,&-2,&0,&3,&4,&10 \end{bmatrix}$$

. Find the results of the following operations by hand and use MATLAB to check your results.

$$a .\quad z = y < \sim x$$

$$b.\quad z = x \& \mathrm { y }$$

$$c .\quad z = x | y$$

$$d .\quad z = \operatorname { xor } ( \mathrm { x } , \mathrm { y } )$$

A force

$$\mathbf { F } = 2 \mathbf { i } + \mathbf { j } - 3 \mathbf { k }$$

is applied to a spacecraft with velocity vector

$$\mathbf { v } = 3 \mathbf { i } - \mathbf { j }.$$

Express

$$mathbf { F }$$

as a sum of a vector parallel to

$$\mathbf { v }$$

and a vector orthogonal to

$$\mathbf { v }.$$

An ideal gas undergoes a reversible isothermal expansion at $132\degree\mathrm{C}$. The entropy of the gas increases by $46.2$ $\mathrm{J/K}$. How much heat is absorbed?

An ideal gas undergoes an isothermal expansion at $77\degree\mathrm{C}$ in- creasing its volume from $1.3$ to $3.4$ $\mathrm{L}$. The entropy change of the gas is $24~\mathrm{J/K}$. How many moles of gas are present?