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?

Expand 1.00 mol of an monatomic gas initially at 8.00 kPa and 600 K from initial volume

$$V _ { i } = 1.00 m ^ { 3 }$$

to final volume

$$V _ { f } = 2.00 \mathrm { m } ^ { 3 }$$

. At any instant during the expansion, the pressure p and volume V of the gas are related by

$$p = 5.00 \exp \left[ \left( V _ { i } - V \right) / a \right]$$

, with p in kilopascals,

$$V_i$$

and V in cubic meters, and

$$a = 1.00 m^3$$

. What are the final (a) pressure and (b) temperature of the gas? (c) How much work is done by the gas during the expansion? (d) What is

$$\Delta S$$

for the expansion? (Use two simple reversible processes to find

$$\Delta S$$

).

Expand 1.00 mol of an monatomic gas initially at 5.00 kPa and 600 K from initial volume $V_i = 1.00$ m$^3$ to final volume $V_f = 2.00$ m$^3$. At any instant during the expansion, the pressure p and volume V of the gas are related by $p = 5.00 \exp[(V_i - V)/a]$, with p in kilopascals, $V_i$ and V in cubic meters, and a = 1.00 m$^3$. What is the final pressure of the gas?

Expand 1.00 mol of an monatomic gas initially at 5.00 kPa and 600 K from initial volume $V_i = 1.00$ m$^3$ to final volume $V_f = 2.00$ m$^3$. At any instant during the expansion, the pressure p and volume V of the gas are related by $p = 5.00 \exp[(V_i - V)/a]$, with p in kilopascals, $V_i$ and V in cubic meters, and a = 1.00 m$^3$. What is the temperature of the gas?

Expand 1.00 mol of an monatomic gas initially at 5.00 kPa and 600 K from initial volume $V_i = 1.00$ m$^3$ to final volume $V_f = 2.00$ m$^3$. At any instant during the expansion, the pressure p and volume V of the gas are related by $p = 5.00 \exp[(V_i - V)/a]$, with p in kilopascals, $V_i$ and V in cubic meters, and a = 1.00 m$^3$. How much work is done by the gas during the expansion?

For

$$A=\left( \begin{array}{ccc}{2} & {1} & {-1} \\ {-1} & {2} & {1} \\ {0} & {6} & {1}\end{array}\right)$$

and

$$\mathbf{B}=\left( \begin{array}{ccc}{4} & {7} & {-3} \\ {-1} & {-2} & {1} \\ {6} & {12} & {-5}\end{array}\right),$$

calculate AB and hence solve the system of equations

$$\left\{\begin{array}{l}{4 a+7 b-3 c=-8} \\ {-a-2 b+c=3} \\ {6 a+12 b-5 c=-15}\end{array}\right.$$

Insert $cup$ or $cap$ to make each statement true .

$$\{0,10\} \text{ \_\_\_\_\_ } \{10,0\} = \{0,10\}$$

The following results on summations will help us in calculating the sample variance

$$s ^ { 2 }$$

. For any constant c,

$$\sum _ { i = 1 } ^ { n } c = n c$$

.

In its monthly report, the local animal shelter states that it currently has 24 dogs and 18 cats available for adoption. Eight of the dogs and 6 of the cats are male. Find each of the following conditional probabilities if an animal is selected at random: The pet is female, given that it is a dog.

A 50.0 g block of copper whose temperature is 200 K is placed in an insulating box with a 100 g block of lead whose temperature is 400 K. (a) What is the equilibrium temperature of the two-block system? (b) What is the change in the internal energy of the system between the initial state and the equilibrium state? (c) What is the change in the entropy of the system?

Let f(x)=x^3+x^2-4x+3 on [-2,2] (a)Use a graphing utility to draw the graph of f (b)Use the trace function to approximate the points on the graph where the tangent line is horizontal (c)Use a CAS to find f'(x) (d)Use a solver to solve the equation f'(x)=0 and compare what you find to what you found in (b)

Blood can carry excess energy from the interior to the surface of the body, where the energy is dispersed in a number of ways. While a person is exercising, 0.6 kg of blood flows to the surface of the body and releases 2000 J of energy. The blood arriving at the surface has the temperature of the body interior,

$$37.0 ^\circ C.$$

Assuming that blood has the same specific heat capacity as water, determine the temperature of the blood that leaves the surface and returns to the interior.

People at stage 6 moral reasoning do not obey laws that go against their conscience. Write a paragraph giving your opinion of what the world would be like if everyone acted in this way.

Find $\nabla(a \cdot r),(a \cdot \nabla) r \text { and } a(\nabla \cdot r)$, where a is a constant vector and, as usual, r is the position vector r = (x, y, z).