Sample Review Problems on Specific Heats, Internal Energy, Enthalpy and Entropy

Hi folks!

Well, thermodynamics is a very great subject for students who are about take up and those who are currently taking up. The good thing about this subject is that you can always connect it to other problems (let say gases and the interesting topic regarding steam and its cycles) since the basic concepts are applied over and over again.

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Today, allow me to share a problem wherein it showcases the thermodynamic properties being exhibited by ideal gases and these properties are as follows: Specific Heat Capacity both at constant volume (C_v) and at constant pressure (C_p), Internal Energy (U) and lastly, Enthalphy (H).

So without further ado, let me start with this first sample review problem and I’m pretty sure you’ll get excited about it and I will show the easiest way in solving for we know there are many ways in killing a cat and does in solving mathematical problems too.

A gas initially at 15 psia and 2 ft³ undergoes a process to 90 psia and 0.60 ft³, during which the enthalpy increases by 15.5 BTU; C_v = 2.44 BTU per lb_m per unit degree Rankine. Determine the following:

• Change in Internal Energy
• Specific Heat Capacity at Constant Pressure (C_p)
• Gas Constant (R)

So let’s start solving this problem.

• Change in Internal Energy
  Since we are provided with the change in enthalpy (delta H) being experienced by the gas, we can directly obtain the change in internal energy (delta U) by using the formula in computing for the enthalpy and the same time we are provided with both the initial and final states of the gas wherein the pressure (P) and volume (V) are explicitly stated. And the calculation goes like this:
  

  
  And therefore, the change in internal energy is equal to 11.06 BTU.

• Specific Heat Capacity at Constant Pressure (C_p)
  As for this one, the easiest way in solving this problem is remembering the relation of both the specific heat capacity at constant volume (C_v) and at constant pressure (C_p) which is also connected to the relation of both the change in enthalpy (delta H) and change in internal energy (delta U). So here is my calculation for this question:
  

  
  Based on the above photo, I simply use both the change in enthalpy and change in internal energy for the very reason that change in enthalpy utilizes the specific heat capacity at constant pressure (C_p) and whereas for the change in internal energy it utilizes the specific heat capacity at constant volume (C_v), and thus since both are experiencing temperature change, we can simply cancel it out and the same happens also with the mass. And therefore the specific heat capacity at constant pressure (C_p) is equal to 3.42 BTU per lb_m per unit degree Rankine.

• Gas Constant (R)
  For this problem, we will just be using the relations for the gas constant (R), the specific heat capacity at constant volume (C_v) and at constant pressure (C_p). And the solution goes like this;
  

  
  As you've noticed above, the gas constant is having two units both of which are in English system of units, the very reason for that is as far as I can remember, the gas constant is always presented in units of ft-lb_f per unit lb_m per unit degree Rankine and whereas for the specific heat capacities whether it is at constant volume (C_v) or at constant pressure (C_p) is always expressed in units of BTU per unit lb_m per unit degree Rankine. And with that we 0.98 BTU per unit lb_m per unit degree Rankine as the gas constant of the gas being used in this problem wherein it is also equal to 762.4 ft-lb_f per unit lb_m per unit degree Rankine.

So I guess that would be all for this sample review problem on specific heats, internal energy and enthalpy.

Thank you for spending your time reading this blog post of mine.

Much love and respect.

Ace | @josephace135

Reference:

1. Hipolito B. Sta. Maria, Thermodynamics
   Solutions are being made by me and the sample review problem is found in page 50, problem number 9.
   Presentation of equations and formulas were made possible by MS Word 2010 Equations function.
   Screenshots were made possible by utilization of Snipping Tool application.