Heat Transfer- A Path Function

Need help with your homework? Look no further! Our subject experts are ready to effortlessly handle your assignments, so you can finally say goodbye to stress and hello to top grades.

Click or drag files to this area to upload. You can upload up to 3 files.
Get a response in under 15 min

The quantity of heat transferred not only depends on the state of the object at the end, but it also depends on the path followed by it. Thus heat transfer can also be called a path function. Thus Q can be written as heat transfer.

Therefore it is an in accurate differential.


Heat Transfer- A Path Function 1


So uneven temperature or the imbalance of heat enhances the transfer the transfer of heat. To be moreevident the difference in temperature causes the heat to flow between the bodies until equilibrium is attained.

Thus heat transfer is mathematically represented by


Heat Transfer- A Path Function 1 2


where T=intensive property and X = extensive property of the substance.

It is applicable only for a quasi-static process only. The quantity of heatbeing  transferred can be calculated from the area under (T, X) coordinates illustration

 dQ = T dX

dX  =dQ / T

 Hereone / T is an integrating factor which is used with inaccurate quantity to create it precisedifferences.

Solved Examples

Example 3.1- Centrifugal pump powers up water horizontally at two m3/min from an open well to a closed tank. The pressure here is 0.45 Mpa. So calculate the work of the pump which it must do to the water in an hour just to strength the water into the tank contrary to the pressure.

Solution.              P = 0.45 x 106 Pa = 450 kPa

dV = 2m3 , time , t = 1 min

= V2 – V1

In one minute work done = ʃ = pd V = P ( V2-V1)

= 450 (2-0) = 900 kNm.

 Thus in one hour, the work was done= 900 x 60 KJ / hr.

= 54000 KJ/hr.

 Example 3.2. A petrol engine cylinder is fitted with a piston of aplane at 0.15 m2  and maintaining its pressure at 2MPa. Thus the gas increasesby a straight line process on the  P – V diagram. Therefore the last pressure remains 0.2 Mpa. NowAnalyse the work done by the gas on the piston if the stroke is 0.15 m.


WI-2 = area under the curve (Straight line) 1-2

= 1/2 [ 2 + 0.2] x 106 x 0.15 x 0.15 Nm

= 24.75 KJ. Ans.

 Example 3.3 – If a mass of 2 kg of air is trampled in a quasi-static process from 0.15 Mpa to 0.75 Mpa for which PV = Const.Then find out the initial density of air which is 1.5 kg/m3. Also, determinethe work done by the piston to compress the air.

 Solution. We have               W1  2 = P1 V1 In P1 / P2

= 0.15

= – 0.15 x 106 x 2 / 1.5 In 0.15 / 0.75 J

= – 0.321888  x 106  J

= – 321.8 KJ

 The negative sign of work confirmations that the work is done on the system.

Example 3.4- A certain amount of gas is trampled in a quasi-equilibrium process from 90 KPa,0.15 m3 to 0.5 MPa, 0.04 m3. Now let us consider that the pressure and volume are connected by PV” =Canst.  So determine the work done on the gas system. (Take n = 1.3)


Heat Transfer- A Path Function 3



   W1 = P1 V1 – P2 –P2 / n-1 = 90 x 103 x 0.15 – 0.5 x 106 x 0.04 J / 1,3 – 1

= – 21.7 Kj.

 Negative sign shows that the work is done on the system.

Example 3.5– Analyze the total work done by a gas system in a expansion process shown in

Fig. 3.12 (1 bar = Uf N/m2)


  W1-2-3 = W1-2 + W2-3

Now                               W1-2 = 50 x 105 x (0.4 -0.2 ) J  = 10 x 105 J [ Note.P1V2 = P3 V3]

W2-3 = P2 V2-P3 V3 / n-1 = P2 V2 / n-1 [ 1 – (P3 / P2) n-1 / n

=P2 V2 / n-1 [ 1 – ( V2 / V3) n-1]

= 50 x105 x 0.4 / 13.1 [ 1- (0.4 / 0.8)0.3]

= 12.516 x 105 J

= 2.2156 x 106 J = 2.2516 MJ. Ans.


Links of Previous Main Topic:-

Links of Next Mechanical Engineering Topics:-

Homework Blues?

Get expert help with homework for all subjects.

  • NPlagiarism-free work
  • NHonest Pricing
  • NMoney-back guarantee

Latest Reviews

Solved Sample Works

Accounting Homework

Corporate Accounting Sample

Biology Homework

Genetics Assignment Sample

Essay Writing Help

Business Plan Sample

Homework Help FAQs

Our Answers to Your Questions

How do I submit my homework?

Getting homework help is very simple with us. Students can either send us the homework via email or they can upload it to our online form here. For a quicker response, You can also chat with us at WhatsApp and submit homework directly. You are sure to get a response from our side within 10 minutes.

How much will my homework cost?

The cost of paying someone to do your homework varies depending on the service and the type of assignment. We have listed our standard pricing plans for popularly used writing services. For other kind of assignments, You can get a free instant quote from us using our online form.

We also accept partial payment to start working on your assignment help. You can pay the remaining amount when your task gets completed. No pressure of up-front payment. No hidden order costs.

Can I receive help with my homework anytime?

Yes, you can receive help with your homework anytime with us. Our online homework help services are available 24/7, allowing you to receive assistance with your homework anytime, anywhere.

For urgent homework requests, reach out to us through our LiveChat or WhatsApp channels and one of our friendly support agents will assist you in finding the right expert for your online homework help request immediately. With our services, you can rely on 24/7 availability and meeting deadlines.

Are online homework websites budget-friendly for students like me?

Yes, Our Online Homework Help websites are an affordable solution for you as a student. Compared to traditional tutoring services, MyHomeworkHelp prices their homework help services honestly and within the budget of college students. This makes it easier for you to receive assistance with your homework without breaking the bank.

What is your plagiarism-free policy?

At myhomeworkhelp, we take plagiarism very seriously and ensure that all solutions provided by our tutors are original and authentic. Our tutors are trained to provide custom-made solutions, tailored specifically to meet the requirements of each student. We do not provide pre-written papers. All our homeswork solutions are made from scratch, guaranteeing 100% orignal homework answers.

Additionally, we have strict plagiarism-detection tools in place to check all submissions for authenticity.

Is using an Online Homework Help Service cheating?

Using online homework help services is not equivalent to cheating. Our services are intended to support students with their homework and provide them with the resources they need to succeed academically. With the help of our online homework help services, students can receive immediate assistance with their homework from any location, at any time.

At myhomeworkhelp, we are committed to promoting academic integrity. Our tutors provide solutions that serve as guides for drafting your own work. It is not acceptable to submit someone else's work as your own, as this constitutes academic plagiarism.

Can I chat with my tutor?

Using our secure chat board, you can now chat directly with your assigned tutor. The chats are encrypted both ways to secure your privacy. This makes your contact with the tutor directly & confidentially, so you can better explain any requirements or changes if needed or just need updates.

You can't contact the experts outside of chat board platform. Sharing any personal information, including but not limited to contact information, goes against our Terms and Conditions and therefore may result in permanently blocking you from the platform. We take any personal data very seriously and we do it for the safety of our users.

Know more about chat board here.

What is your money-back guarantee policy?

It’s worth noting that our online homework help service rarely leads to disappointment among students. Our expert tutors, along with our support and quality assurance team, are dedicated to providing the best possible experience for our customers. However, if for any reason a student is unsatisfied with their homework help solution, we offer unlimited revisions until they are fully satisfied.

In the rare event that a student remains unsatisfied even after revisions, we offer a money-back guarantee. We want all of our students to feel confident and secure when they turn to us for assistance with their homework, and this guarantee is just one way that we demonstrate our commitment to providing the best possible service. If you have any concerns about our services or the quality of the work you receive, please contact us for support.

What is the expertise of the tutor assigned to do my homework?

At myhomeworkhelp, we take pride in our team of qualified and experienced tutors. All of our tutors undergo a rigorous selection process and are required to have a minimum of a master's degree in their respective fields. Additionally, they must pass a series of tests to demonstrate their proficiency and ability to deliver quality work. We believe in transparency and providing our clients with the best possible service. You can be confident in the expertise of the tutor assigned to do your homework.

What about privacy & confidentiality?

Using My Homework Help is absolutely safe. We care about your security, therefore we encrypt all personal data to make every user feel safe while using our services and we don’t share any personal information with any third parties without your permission. Your credit card information is not stored anywhere at My Homework Help, and use of PayPal relies on their secure payment networks. Your identity, payment and homework are in safe hands. You can always be certain of getting professional help and remaining anonymous, while using My Homework Help.