### Problem Statement1.67. A gas contained within a piston-cylinder assembly, initially at a volume of 0.4 m³, undergoes a constant-pressure expansion at 5 bar, while being slowly heated through the base of the cylinder. During this process, the total amount of heat transfer to the gas is 150 kJ and the increase in potential energy of the piston is 75 kJ. The piston is fabricated from heat-resistant material and it moves smoothly in the cylinder so that there is no friction. Assume that the local atmospheric pressure is 1 bar.**Questions:**a. **Find the final volume of the gas, in m³.**b. **Calculate the boundary work done by the gas, in kJ.**c. **If the initial internal energy (U1) of the gas is 15 kJ, what will be its final internal energy (U2), in kJ?**### Explanation:The problem involves applying principles of thermodynamics to a piston-cylinder system. This system experiences a constant-pressure expansion due to heating. - **Initial Volume (V1):** 0.4 m³- **Pressure:** 5 bar- **Heat Transfer (Q):** 150 kJ- **Increase in Potential Energy (ΔPE):** 75 kJ- **Initial Internal Energy (U1):** 15 kJ**Objective:** Solve for the final volume, boundary work, and final internal energy.### Solving the Problem:**a. Final Volume:**Use the ideal gas law or given conditions for calculations knowing there's a constant-pressure process.**b. Boundary Work:**Boundary work (W) in a piston system at constant pressure can be calculated as:\[ W = P \times (V_2 - V_1) \]Rearrange the equation as necessary based on known values.**c. Final Internal Energy:**Use the first law of thermodynamics:\[ \Delta U = Q - W + \Delta PE \]Substitute known quantities to solve for the change in internal energy, then find $ U2 = U1 + \Delta U $.

Answered: Image /qna-images/answer/1cce8cb0-2531-4076-98d0-79ebe01102fa.jpg

1.67. Given that a gas contained within a piston-cylinder assembly, initially at a volume of 0.4 m3, undergoes a constant-pressure expansion at 5 bar, while being slowly heated through the base of the cylinder. During this process, the total amount of heat transfer to the gas is 150 kJ and increase in potential energy of the piston is 75 kJ. The piston is fabricated from heat-resistant material and it moves smoothly in the cylinder so that there is no friction. Assume that the local atmospheric pressure is 1 bar. a. Find the final volume of the gas, in m3. b. Calculate the boundary work done by the gas, in kJ. c. If initial internal energy (U1) of the gas is 15 kJ, what will be its final internal energy (U2), in kJ?

1.67. Given that a gas contained within a piston-cylinder assembly, initially at a volume of 0.4 m3, undergoes a constant-pressure expansion at 5 bar, while being slowly heated through the base of the cylinder. During this process, the total amount of heat transfer to the gas is 150 kJ and increase in potential energy of the piston is 75 kJ. The piston is fabricated from heat-resistant material and it moves smoothly in the cylinder so that there is no friction. Assume that the local atmospheric pressure is 1 bar. a. Find the final volume of the gas, in m3. b. Calculate the boundary work done by the gas, in kJ. c. If initial internal energy (U1) of the gas is 15 kJ, what will be its final internal energy (U2), in kJ?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: Determine the rate at which the energy is removed by heat transfer from the refrigerated space, in…

A: The power input to refrigerator is The heat rejected to surrounding is

Q: Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be…

A: Given Mass, m = 5 kg Initial temperature, T1 = 427oC Initial pressure,…

Q: ir is contained in a vertical piston–cylinder assembly by a piston of mass 50 kg and having a face…

A: Given:Mass of piston, mp=50 kgArea of the piston, A=0.01 m2Mass of air, m=5 g =0.005 kgInitial…

Q: 3. 8.0 MJ of work is inputted to isothermally move a 1500 Kg mass from an elevation of zero to 35m…

A: Given data as per question

Q: It is a hot day in Atlanta and you and your friends bought an ice cream maker. The unit consists of…

A: To obtain the solution of the above question, we will apply the 1st law of thermodynamics and is…

Q: 1. An "empty" propane tank is brought to a filling station to be reloaded. The tank is a standard…

A: Given:The total volume of the tank, The temperature of saturated propane vapor in the empty tank is…

Q: Q2. SO parts A reversed reversible heat engine extracts heat 01-22 from a cold reservoir at…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Steam generators are a type of heat exchanges that are used in power plants to generate steam at…

Q: A mass of 6.7 kg of steam is contained within a piston-cylinder assembly. The steam undergoes an…

Q: The figure below shows a gas contained in a vertical piston-cylinder assembly. A vertical shaft…

A: \GivenPatm=1 barshaft cross sectionalarea(As)=0.8 cm2As=8×10-5 m2mass of piston (mp)=30 kgmass of…

Q: A reaction which requires the input of thermal energy is called a

Q: Consider the PV diagram as shown above when a thermodynamic system changes its state from state a to…

Q: A gas is contained in a vertical piston-cylinder assembly by a piston with a face area of 50 in² and…

Q: A fixed mass of gas undergoes changes of pressure and volume as shown below.

A: Given: Some process are there,Process PQ=8 kJ heat are absorbed,Process QR=3 kJ of work is…

Q: Calculate the change in internal energy (in kJ) when a 5 kg Cast Iron pot is heated from 20°C (65°F)…

Q: Steam generators are a type of heat exchanges that are used in power plants to generate steam at…

A: Inlet Velocity of the steam is 4.24 m/s.

Q: 3.75 Three lb of water is contained in a piston-cylinder assembly, initially occupying a volume V₁ =…

Q: In the United States, energy for household heating is generally sold using English units, e.g.,…

A: Given:The efficiencies are based on the HHV. Assume the cost of natural gas is $8/MBtu, the cost of…

Q: 3. A work done on the steady flow system is 30 kJ/kgm. Calculate the heat in HP if the mass flow…

A: Given:W=-30 KJ/Kgm=10 Kg/minu1=10 KJ/Kgu2=20 KJ/Kg

Q: 3.76 A system consisting of 2 kg of ammonia undergoes a cycle composed of the following processes:…

A: The basic assumptions to be considered for the cycle: The cycle is a closed system Kinetic and…

Q: 3. The movement of a piston in a cylinder is restrained by a spring with a spring constant…

A: Given Data⇒Spring constant K=250 lbinAt a position x=0 F=0 lbfProblem definition⇒Problem says…

Q: creases from zero to Assuming a constant

Q: Steam generators are a type of heat exchanges that are used in power plants to generate steam at…

A: Given data Water enters at 30°C Diameter of tube = 60 mmVolume flow rate = 12 L/s = 12 x 10-3…

Q: 2.13 A gas expands from an initial state where p 500 kPa and V= 0.1 m² to a final state where P₂ =…

A: Given data: P1=500 KpaP2=100 KpaV=0.1 m3PV=constant

Concept explainers

Basic Terminology in Mechanics

The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its environment. This branch of physics keeps its roots in Ancient Greece in the form of the scripts of Aristotle and Archimedes.

Question

### Problem Statement

1.67. A gas contained within a piston-cylinder assembly, initially at a volume of 0.4 m³, undergoes a constant-pressure expansion at 5 bar, while being slowly heated through the base of the cylinder. During this process, the total amount of heat transfer to the gas is 150 kJ and the increase in potential energy of the piston is 75 kJ. The piston is fabricated from heat-resistant material and it moves smoothly in the cylinder so that there is no friction. Assume that the local atmospheric pressure is 1 bar.

**Questions:**

a. **Find the final volume of the gas, in m³.**

b. **Calculate the boundary work done by the gas, in kJ.**

c. **If the initial internal energy (U1) of the gas is 15 kJ, what will be its final internal energy (U2), in kJ?**

### Explanation:

The problem involves applying principles of thermodynamics to a piston-cylinder system. This system experiences a constant-pressure expansion due to heating.

- **Initial Volume (V1):** 0.4 m³
- **Pressure:** 5 bar
- **Heat Transfer (Q):** 150 kJ
- **Increase in Potential Energy (ΔPE):** 75 kJ
- **Initial Internal Energy (U1):** 15 kJ

**Objective:** Solve for the final volume, boundary work, and final internal energy.

### Solving the Problem:

**a. Final Volume:**

Use the ideal gas law or given conditions for calculations knowing there's a constant-pressure process.

**b. Boundary Work:**

Boundary work (W) in a piston system at constant pressure can be calculated as:

\[ W = P \times (V_2 - V_1) \]

Rearrange the equation as necessary based on known values.

**c. Final Internal Energy:**

Use the first law of thermodynamics:

\[ \Delta U = Q - W + \Delta PE \]

Substitute known quantities to solve for the change in internal energy, then find $ U2 = U1 + \Delta U $.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1 Analysis and calculation

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

.
Please help! Thank u! 3. Consider the following systems. a) What is the heat capacity of a system consisting of a 0.870-kg brass cup filled with 0.0500 kg of water? Specific heats of brass and water at 1.00 atm and 20.0°C are 0.384 kJ/kg•K and 4.186 kJ/kg/K respectively. b) What is the heat capacity of a system consisting of 8.10 kg of water in a 0.310-kg aluminum bucket? Specific heats of aluminum and water at 1.00 atm and 20.0°C are 0.900 kJ/kg-K and 4.186 kJ/kg:K respectively.
A piston-cylinder contains nitrogen initially at 100 kPa, 20°C, and a volume of 0.283 m³ (State 1). The nitrogen undergoes two processes. First, the nitrogen is compressed to 7000 kPa (State 2) in an isothermal process. Finally, the nitrogen is expanded to 100 kPa (State 3) in a reversible adiabatic process. You may assume that nitrogen is an ideal gas with constant (average) specific heats: Cp = 1.039 kJ/kgK, c, = 0.742 kJ/kgK, and R= 0.297 kJ/kgK.
2. Air is contained in a piston-cylinder assembly and is compressed between an initial and final state. For each of the following cases, determine whether it is possible for the process to occur adiabatically. If it can, determine the work per unit mass required for the process (use units appropriate for those provided in the process). If not, determine the direction of heat transfer (in/out of system). For the purposes of this problem, air can be modelled as an ideal gas. a. P1 = 1 bar, T = 27°C → P2 = 5 bar, T2 = 217°C b. P= 40 psi, T = 80°F → P2 = 150 psi, T2 =240°F
4.13. Consider using the apparatus shown in Fig. 4-1(a), known as the Joule paddle wheel, to determine the specific heat at constant atmospheric pressure. The paddle wheel is driven by a slowly falling weight, and both have a temperature of 14.5°C. As a result of the work done by the 0.427 kg mass that falls 1.00 m, the temperature of 1 kg of water rises 1°C. Calculate cp.
Steam generators are a type of heat exchanges that are used in power plants to generate steam at desired pressure and temperature (Fig. Q1.b). In a steam generator, saturated liquid water at 30°C enters a 60-mm diameter tube at the volume flow rate of 12 L/s. After exchanging heat with hot gas, the water changes to steam and leaves the generator at a pressure of 9 MPa and a temperature of 400°C. During this process, the diameter of the water/steam tube does not change.(iii) What is the exit velocity of the steam?
1.6 World energy consumption reached about 500 quadrillion Btus in 2010. Estimate the equivalent energy quantities in: barrels of oil, metric tons (tonnes) of coal, standard cubic feet of natural gas, gallons of reservoir water elevated 1000 m above sea level, kilograms of steam (saturated vapor) at 200°C, kilograms of hot water (saturated liquid) at 200°C, cubic meters of granite at 250°C.
2.44 As shown in Fig. P2.44, the 6-in.-thick exterior wall of a building has an average thermal conductivity of 0.32 Btu/h ft °R. At steady state, the temperature of the wall decreases linearly from T to T, on the outer surface. The outside ambient air temperature is To coefficient is 5.1 Btu/h ft °R. Determine (a) the temperature T in °F, and (b) the rate of heat transfer through the wall, in Btu/h per ft of surface area. 70°F on the inner surface 25°F and the convective heat transfer
Question No 4: A 4-kW resistance heater in a water heater runs for 2 hours to raise the water temperature to the desired level. Determine the amount of electric energy used in both kWh and kJ.
2,3) In a plunger cylinder device, 15 kg of air is heated from 25°C to 77°C by passing current through a resistance heater inside the cylinder. The initial pressure in the cylinder is 300 kPa and in the process 60 kJ of heat is lost to the environment. Determine the electrical energy supplied during the process and express it in units of kWh.
A fixed mass of gas undergoes changes of pressure and volume as shown below. V When the gas is taken from state P to state R by stages PQ and QR, 8 kJ of heat are absorbed by it and 3 kJ of work are done by it. When the same resultant change is achieved by stages PS and SR, 1 kJ of work is done by the gas. In this case which of the following represents the heat transfer? Select one: 8 kJ of heat are absorbed b. 4 kJ of heat are rejected 12 kJ of heat are rejected O d. 10 kJ of heat are absorbed
Using 1st and 2nd law of thermodynamics for irreversible expansion of Krypton: Krypton (ideal monatomic gas) is confined in one-fourth of a 48-litre container. The other part of the container is evacuated. When the partition is removed, the gas expands and fills the whole container, while the system loses 400J of heat to the environment at 290K. It is found that in the final state, the Krypton is at p2 = 5.5bar, T2 = 400K. Is this process possible or not? (?k?????? = 83.8 kg/kmol)