A container is filled with an ideal diatomic gas to a pressure and volume of P1 and V1, respectively. The gas is then warmed in a two-step process that increases the pressure by a factor of five and the volume by a factor of four. Determine the amount of energy transferred to the gas by heat if the first step is carried out at constant volume and the second step at constant pressure. (Use any variable or symbol stated above as necessary.)

A container is filled with an ideal diatomic gas to a pressure and volume of P1 and V1, respectively. The gas is then warmed in a two-step process that increases the pressure by a factor of five and the volume by a factor of four. Determine the amount of energy transferred to the gas by heat if the first step is carried out at constant volume and the second step at constant pressure. (Use any variable or symbol stated above as necessary.)

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter17: Energy In Thermal Processes: The First Law Of Thermodynamics

Section: Chapter Questions

Problem 76P

See similar textbooks

Similar questions

One of a dilute diatomic gas occupying a volume of 10.00 L expands against a constant pressure of 2.000 atm when it is slowly heated. If the temperature of the gas rises by 10.00 K and 400.0 J of heat are added in the process, what is its final volume?
One process for decaffeinating coffee uses carbon dioxide ( M=44.0 g/mol) at a molar density of about 14,0 mol/m3 and a temperature of about 60 . (a) Is CO2 a solid, liquid, gas, or supercritical fluid under those conditions? (b) The van der Waals constants for carbon dioxide are a=0.3658 Pa m6/mol2 and b=4.286105 m3/mol. Using the van der Waals equation, estimate pressure of CO2 at that temperature and density. `
As shown below, calculate the work done by the gas in the quasi-static processes represented by the paths (a) AB; (b) ADB; (c) ACB; and (d) ADCB. `
A dilute gas at a pressure of 2.0 atm and a volume of 4.0 L is taken through the following quasi-static steps: (a) an isobaric expansion to a volume of 10.0 L, (b) an isochoric change to a pressure of 0.50 atm, (c) an isobaric compression to a volume of 4.0 L, and (d) an isochoric change to a pressure of 2.0 atm. Show these steps on a PV diagram and determine from your graph the net work done by the gas.
The insulated cylinder shown below is closed at both ends and contains an insulating piston that is flee to move on frictionless bearings. The piston divides the chamber into two compartments containing gases A and B. Originally, each compartment has a volume of 5.0102 m3 and contains a monatomic ideal gas at a temperature of and a pressure of 1.0 atm. (a) How many moles of gas are in each compartment? (b) Heat Q is slowly added to A so that it expands and B is compressed until the pressure of both gases is 3.0 atm. Use the fact that the compression of B is adiabatic to determine the final volume of both gases. (c) What are their final temperatures? (d) What is the value of Q?
An amount of n moles of a monatomic ideal gas in a conducting container with a movable piston is placed in a large thermal heat bath at temperature T1 and the gas is allowed to come to equilibrium. After the equilibrium is leached, the pressure on the piston is lowered so that the gas expands at constant temperature. The process is continued quasi-statically until the final pressure is 4/3 of the initial pressure p1 . (a) Find the change in the internal energy of the gas. (b) Find the work done by the gas. (c) Find the heat exchanged by the gas, and indicate, whether the gas takes in or gives up heat.
Two moles of a monatomic ideal gas at (5 MPa, 5 L) is expanded isothermally until the volume is doubled (step 1). Then it is cooled isochorically until the pressure is 1 MPa (step 2). The temperature drops in this process. The gas is now compressed isothermally until its volume is back to 5 L, but its pressure is now 2 MPa (step 3). Finally, the gas is heated isochorically to return to the initial state (step 4). (a) Draw the four pi-cresses in the pV plane. (b) Find the total work done by the gas.
When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV to the power of 1.4 = C where C is a constant. Suppose that at a certain instant the volume is 480 cubic centimeters and the pressure is 75 kPa and is decreasing at a rate of 10 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant? Please Write legible
If you have 9 moles of a monoatomic ideal gas, how much heat is required to raise the temperature of this gas from 264.3K to 277.6K if the volume of the gas remains constant during the heating? Note: It is understood that your answer is in units of Joules
Boyles Law states that when a sample of gas is compressed at a constant temperature, the product of the pressure and the volume remains constant: PV=C. A. Find the rate of change of volume with respect to pressure. B. A sample of gas in a container at low pressure and is steadily compressed at constant temperature for 10 minutes. Is the volume decreasing more rapidly at the beginning or the end of the 10minutes? Please Explain.. C. Prove that the isothermal compressibility is given by B=1/P.
A mole of an ideal gas of vibrating diatomic molecules at initial temperature T is expanded from an initial volume V to a final volume 2V in an isobaric process. Using the convention that heat is positive when it is absorbed by the system, what is the heat transfer Q in this process in terms of R and T?
The Joule-Kelvin coefficient that determines the performance of a gas in a throttling process is defined as μ_JK = (∂T/∂p)_H where H is enthalpy. Show that μ_JK= 0 for an Ideal Gas. [HINT: You will need to form an expression for H, and use the differential calculus cyclic relation to correctly form this partial derivative for μJK]