Thermodynamics Review Problems for Mechanical Engineering Students | Series 6

in #steempress6 years ago

Hi folks!

This is the 6th series of my "Thermodynamics Review Problems for Mechanical Engineering Students". This series features two problems for which the first one is about the boundary work for a hydrogen gas which is in a piston-cylinder device and the other one is simply using the continuity equation in conjunction with the universal gas constant. Without much ado, lets get it on!

Review Problem 1

A piston-cylinder device contains 1 kilogram of hydrogen gas. Heat is transferred to the hydrogen as its temperature increases by 10 degree Celsius. What is the boundary work done during this process?

Solution

For this review problem, since we are only provided with both the temperature change and the mass of hydrogen gas in the piston-cylinder device and at the same time, we cannot say that the piston-cylinder device is a constant volume or constant pressure process – so the only way to solve this problem is to use the provided thermodynamic properties. With that in mind, we will just express this boundary work as a function of mass, gas constant and temperature change. For the gas constant of hydrogen, we will just use the general formula R = 8.314/MW for which the MW (molecular weight) of hydrogen gas is 2 kg/kmol, and the explanation for that why it has 2 as its MW, it’s because hydrogen gas is a diatomic molecule. And with that the gas constant for hydrogen gas is equal to 4.157 kilojoule per kilogram per degree Kelvin. And for the boundary work being done during the process for which the hydrogen gas increased its temperature by 10 degree Celsius, we simply multiply the mass, the gas constant of hydrogen and the temperature rise. Thus, the boundary work done during the temperature increase is equal to 41.57 kilojoule, say 42 kilojoule.

Review Problem 2

Air enters an adiabatic, steady-flow turbine at 1 mega-pascal and 527 degree Celsius through a one square meter duct with a velocity of 100 meters per second. The air leaves the turbine at 100 kilo-pascal and 157 degree Celsius. The mass flow rate of the air in kilogram per second is:

Solution

For this review problem, the very first thing to obtain is the volume flow rate of the air Q. The formula for the volume flow rate is Q = Av; for which A is the area of the medium for which the air or any fluid enters and v is the velocity of the substance as it enters the medium. And with that, the volume flow rate Q is equal to 100 cubic meters (m3).

Finally, we can now obtain the mass flow rate of the air by using the universal gas constant formula PQ = ṁRT, where Q is the volume flow rate and ṁ is the mass flow rate. Thus, we’re able to compute that the mass flow rate of the air entering and leaving the turbine is equal to 435.54 kilograms per seconds.


Curriculum


Reference

  • PIPE - PROBLEM SET #2 number 11 and 12 by Alcorcon Engineering Review Center

Computations and screenshots are made by the author.

Special thanks to @jbeguna04 for designing the GIF photos.



Posted from my blog with SteemPress : https://geuseppedeacenet.000webhostapp.com/2018/07/thermodynamics-review-problems-for-mechanical-engineering-students-series-6

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