Thermodynamics - Pressure Question

[Icetray]

[SOLVED] Thermodynamics - Pressure Question

Homework Statement

A pressure cooker cooks a lot faster than an ordinary pan by maintaining a higher pressure and temperature inside. The lid of a pressure cooker is well sealed, and steam can escape only through and opening in the middle of the lid. A separate metal piece , the petcock, sits on top of this opening and prevents steam from escaping until the pressure force overcomes the weight of the petcock. The periodic escape of the steam in this manner prevents any potentially dangerous pressure buildup and keeps the pressure inside at a constant value. Determine the mass of the petcock of a pressure cooker whose operations pressure is 100 KPa gage and has an opening cross-sectional area of 4 mm^2 . assume an atomspheric pressure of 101 KPa, and a draw of the petcock


My Question:

I already have the solution to this question and it is stated that:

Atmospheric pressure is acting on all surfaces of the petcock, which balances itself out. Therefore, it can be disregarded in calculations if we use the gage pressure as the cooker pressure. A force balance on the petcock (ƩFy = 0) yields

Here is the diagram given:

If the atmpospheric pressure is still pushing down on the petcock, how can we just ignore it?


Thanks in advance!

 

[Andrew Mason]

If the atmpospheric pressure is still pushing down on the petcock, how can we just ignore it?

You don't ignore it. You just do not have to take it into account explicitly if you use the gage pressure in the pot. The gage pressure takes it into account for you.

The actual pressure in the pot is P_actual = P_gage + P_atm.

AM

 

[Icetray]

You don't ignore it. You just do not have to take it into account explicitly if you use the gage pressure in the pot. The gage pressure takes it into account for you.

The actual pressure in the pot is P_actual = P_gage + P_atm.

AM

Thanks for your reply Andrew Mason!

So basically whenever the term gauge pressure is used, it gives you the difference between the internal and atmospheric pressure?

I thought that was P$_{vacuum}$? My notes shows a diagram of P$_{vacuum}$ and P$_{guage}$. The P$_{vacuum}$ one shows like it gives you the resultant pressure between the atmosphere and the internal pressure (image below) which looks more like what we have in the diagram in my first post.

I apologize if I'm not making any sense but I'm still very lost even though I understand what you're saying. ):

 

[Redbelly98]

So basically whenever the term gauge pressure is used, it gives you the difference between the internal and atmospheric pressure?

I thought that was P$_{vacuum}$?

As your diagram says:
$$P_{gauge} = P_{abs}-P_{atm}$$
$$P_{vac} = P_{atm}-P_{abs}$$
So, while P_gauge and P_vac both "give the difference between internal (abs) and atmospheric pressure", they are not the same.

 

[Icetray]

As your diagram says:
$$P_{gauge} = P_{abs}-P_{atm}$$
$$P_{vac} = P_{atm}-P_{abs}$$
So, while P_gauge and P_vac both "give the difference between internal (abs) and atmospheric pressure", they are not the same.

Ah! I feel so silly now. :-X Anyways thanks guys! (: