A cylinder contains 0.250 mol of carbon dioxide (CO2)gas at a temperature of 27.0?C. The cylinder is provided with a frictionless piston, which maintains a constant pressure of 1.00 atm on the gas. The gas is heated until its temperature increases to 127.0?C. Assume that the CO2 may be treated as an ideal gas.

a.) How much work W is done by the gas in this process?

b.) What is the change in internal energy ?U of the gas?

c.) How much heat Q was supplied to the gas?

The following problem description applies also to the next two problems.

A piston-cylinder device contains 2 kg of a saturated liquid mixture at an initial state 1 with p₁= 100 kPa and x₁= 0.8. The water is heated at constant pressure until its final state 2 with volume V₂ = 1.947V₁.

Its initial volume, in m³/kg, is closer to:

Its final temperature, in ^oC, is closer to:

The amount of heat supplied to the steam during the expansion process, in kJ, is closer to:

0.5 kg of air at 30 bar and 350 °C is allowed to expand reversibly in a cylinder behind a piston in such a way that the temperature remains constant to a pressure of 0.75 bar. Based on the law pv1.05= constant, the air is then compressed until the pressure is 10 bar. Assuming air to be a perfect gas, determine the:

a) net entropy change,
b) net heat flow,
c)net work energy transfer and sketch the processes on a T-s diagram, indicating the area, which represents the heat flow.

Problem 1: A 5.2-liter, spark-ignition, four-stroke cycle, V6 automobile engine operates at 2400 RPM with ? = 1.5. The engine has a volumetric efficiency of 89%, with bore as B = 2.1 S. The density of air at room temperature is 1.18 kg/m3.

Lamda = 1.5

Calculate:

1. Stroke length (m and cm)
2. Average piston speed (m/sec)
3. Mass flow rate of air into engine [kg/sec]
4. Mass flow rate of fuel into engine [kg/sec]

One kilogram of boiling water is vaporized to steam at 100 kPa in a frictionless piston-and-cylinder device. Using the Steam Tables, answer the following:

1. Is the heat needed to vaporize the water to steam equal to the change in enthalpy? Or TDS?
2. To calculate the work done by the steam, is the first law of thermodynamics equation or the general equation for work applicable?
3. Is the entropy generation equal to the change in entropy of the water?
4. Does the heat required for the vaporization of boiling water greater than the work done?

Support your answers with calculations and explanations.

A mixture of 4.00 gram-moles of benzene and 6.00 gram-moles of toluene are placed in a closed cylinder equipped with a piston. The cylinder is immersed in a bath of boiling water that maintains the temperature at 100.0°C. The force exerted on the piston can be varied to adjust the cylinder pressure to any desired values. The pressure is initially 1300 mm Hg and is gradually lowered to 600 mm Hg. Use the Pxy diagram below to convince yourself that the cylinder initially contains only liquid benzene and toluene and to answer the following questions. Carefully read the diagram. The solution can be sensitive to small errors.

At what pressure does the first vapor bubble form?    in mm Hg. What is its composition?    mol benzene/mol

At what pressure does the last droplet of liquid evaporate? in mm Hg. What is its composition?    mol benzene/mol

What are the liquid and vapor compositions in equilibrium with each other when the pressure is 800 mm Hg?

Vapor:    mol benzene/mol

Liquid:    mol benzene/mol .

What is the ratio (mole vapor/mole liquid) at this point?

Estimate the volume of the cylinder contents when the pressure is 1300 mm Hg, 800 mm of Hg, and 600 mm Hg.

1300 mm Hg: in L

800mm of Hg: in L

600 mm Hg: in L

Solve the following

1. Represent the process on a P-V graph.
2. Did the atmosphere do positive, negative or zero work on the system? How do you know?
3. Was the energy supplied to the system through heating positive, negative or zero? How do you know?
4. Was the internal energy change of the system positive, negative or zero? How do you know?
5. Represent the process with an energy bar chart.
6. Ideal Gas in a container with a movable piston at room temperature was put into a hot water container. The gas expanded moving the piston. The gas is our system.

7) You add 25 g of milk at 10^o C to 200 g of coffee (essentially water) at 70^o C. The coffee is in a Styrofoam cup. If the specific heat of milk is 3800 J/kg*^oC, by how much will the coffee temperature decrease when the milk is added? Indicate any assumptions you made. The specific heat of water is 4180 J/kg*^oC,

8) The kayak of a 70-kg man tips and he falls into a cold stream. When he is rescued from the cold water, his body temperature is 33 °C (91.4 °F). He is placed in 50 kg of warm bath water at temperature 41 °C (105.8 °F). What is the final temperature of the man and the water?

7. This scenario can be modeled as a

(a) normal experiment with 4 trials and success probability of 1/6 per trial.

(b) normal experiment with 6 trials and success probability of 1/4 per trial.

(c) binomial experiment with 6 trials and success probability of 1/5 per trial.

(d) binomial experiment with 4 trials and success probability of 1/6 per trial.

(e) binomial experiment with 6 trials and success probability of 1/4 per trial.

8. Complete the following table that represents the probability distribution of

X

= the number of

questions Han guesses correctly.

x

0

1

2

3

4

5

6

P(X = x)

(a) 1/7, 2/7, 3/7, 4/7, 5/7, 6/7, 1

(b) .1780, .5339, .8306, .9624, .9954, .9996, 1

(c) 1/7, 1/7, 1/7, 1/7, 1/7, 1/7, 1/7

(d) .1780, .3560, .2966, .1318, .0330, .0044, .0002

(e) 1/6, 1/6, 1/6, 1/6, 1/6, 1/6

9. What is the probability he will answer at least 4 of the questions correctly?

(a) 0.0376 (b) 10/12 (c) .67% (d) 2/12 (e) 0.0046

10. What is the mean number of questions he will answer correctly?

(a) 0 (b) 1 (c) 1.5 (d) 2 (e) 4

11. What is the standard deviation of the number of questions he will answer correctly?

(a) 0.46 (b) 1 (c) 1.06 (d) 1.5 (e) 1.6

C++, Complete this program as directed

// This program will read in a group of test scores (positive integers from 1 to 100)
// from the keyboard and then calculate and output the average score
// as well as the highest and lowest score. There will be a maximum of 100 scores.
// PLACE YOUR NAME HERE
#include <iostream>
using namespace std;
typedef int GradeType[100]; // declares a new data type:
// an integer array of 100 elements
float findAverage (const GradeType, int); // finds average of all grades
int findHighest (const GradeType, int); // finds highest of all grades
int findLowest (const GradeType, int); // finds lowest of all grades
int main()
{
GradeType grades; // the array holding the grades.
int numberOfGrades; // the number of grades read.
int pos; // index to the array.
float avgOfGrades; // contains the average of the grades.
int highestGrade; // contains the highest grade.
int lowestGrade; // contains the lowest grade.
// Read in the values into the array
pos = 0;
cout << "Please input a grade from 1 to 100, (or -99 to stop)" << endl;

cin >> grades[pos];
while (grades[pos] != -99)
{
// Fill in the code to read the grades
}
numberOfGrades = ; // Fill blank with appropriate identifier
// call to the function to find average
avgOfGrades = findAverage(grades, numberOfGrades);
cout << endl << "The average of all the grades is " << avgOfGrades << endl;
// Fill in the call to the function that calculates highest grade
cout << endl << "The highest grade is " << highestGrade << endl;
// Fill in the call to the function that calculates lowest grade
// Fill in code to write the lowest to the screen
return 0;
}
//********************************************************************************
// findAverage
//
// task: This function receives an array of integers and its size.
// It finds and returns the average of the numbers in the array
// data in: array of floating point numbers
// data returned: average of the numbers in the array
//
//********************************************************************************
float findAverage (const GradeType array, int size)
{
float sum = 0; // holds the sum of all the numbers
for (int pos = 0; pos < size; pos++)
sum = sum + array[pos];
return (sum / size); //returns the average

}

//****************************************************************************
// findHighest
//
// task: This function receives an array of integers and its size.
// It finds and returns the highest value of the numbers in the array
// data in: array of floating point numbers
// data returned: highest value of the numbers in the array
//
//****************************************************************************
int findHighest (const GradeType array, int size)
{
/ Fill in the code for this function
}
//****************************************************************************
// findLowest
//
// task: This function receives an array of integers and its size.
// It finds and returns the lowest value of the numbers in the array
// data in: array of floating point numbers
// data returned: lowest value of the numbers in the array
//
//****************************************************************************
int findLowest (const GradeType array, int size)
{
// Fill in the code for this function
}