Questions about the ideal gas law - thermodynamics

[dealz]

im studying building systems engineering technology. yeh i know it's only a technology program at the cegep level but when I'm done with it, I'm going to do software engineering in university. anyways I'm having trouble to understand two problems in the book. if anyone can help me with this, it would be greatly appreciated.

1) Determine the gage pressure if the atmospheric pressure is 14.7 psia, the gas constant is 96 ft-lb/lb R, and the specific volume is 10 ft^3/lbm.
The answer is 31.9 psig

2) 70 lbs mass of gas are contained in a rigid container at 200 psia and 80 F. The gas is then expanded to fill a 2000 ft^3 volume at a pressure pf 20 psia and a temperature of 70 F. Determine the volume of the rigid container.
The answer is 203.7 ft^3.

Can someone show me the steps on how they got the answer because i already know the answer. i just need help on how to solve the problem.

for the first question, the formula is pv = mrt. we'll i know right away to find P = mRT. i would multiply 96ft-lb*700 * R (I don't know how to get that)/ Volume (I also don't know how to get that but i know it's something to do with the specific volume of 10 ft^3)

for the second question, i multiplied (70)(80)/200. and from there I'm lost and don't know what to do.

 

[Nate810]

For the first question, you can use the ideal gas law to solve for the pressure. The equation is P*V = n*R*T, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. You know that the atmospheric pressure is 14.7 psia, the gas constant is 96 ft-lb/lb R, and the specific volume is 10 ft^3/lbm. We can rearrange the equation to solve for pressure, so P = (n*R*T)/V. Plugging in the given values, we get P = (96 ft-lb/lb R * 700 K)/10 ft^3/lbm, which simplifies to P = 672 ft-lb/lbm. Converting this to psi, we get P = 672 ft-lb/lbm * 1 psi/144 ft-lb/lbm, which simplifies to P = 31.9 psi. For the second question, the formula to use is PV = mRT, where P is the pressure, V is the volume, m is the mass, R is the gas constant, and T is the temperature in Kelvin. We can rearrange the equation to solve for volume, so V = (mRT)/P. Plugging in the given values, we get V = (70 lbs * 80 F * 4.66 lb ft/lb R * 518.7 R)/200 psi, which simplifies to V = 203.7 ft^3.

 

[m2003]

Hello,

I am happy to help you understand the ideal gas law and how to solve these problems. The ideal gas law is a fundamental equation in thermodynamics that describes the behavior of gases under certain conditions. It states that the pressure (P), volume (V), temperature (T), and number of moles (n) of a gas are all related by the equation PV = nRT, where R is the gas constant.

Now, let's break down the steps to solve these problems:

1) Determine the gage pressure if the atmospheric pressure is 14.7 psia, the gas constant is 96 ft-lb/lb R, and the specific volume is 10 ft^3/lbm.

To solve this problem, we will use the ideal gas law equation. We are given the values for atmospheric pressure (P = 14.7 psia), gas constant (R = 96 ft-lb/lb R), and specific volume (V = 10 ft^3/lbm). We are asked to find the gage pressure (P_g).

First, let's rearrange the ideal gas law equation to solve for P_g:
P_g = (nRT)/V

Next, we need to find the number of moles (n) of the gas. To do this, we can use the formula n = m/M, where m is the mass of the gas (which is not given in this problem) and M is the molar mass of the gas. Since we do not have the molar mass of the gas, we can assume it to be 1 lbm (pound-mass) for simplicity.

Therefore, n = (m/1 lbm) = m

Now, we can plug in the given values into our equation:
P_g = (mRT)/V

Since we do not have the mass (m) of the gas, we can cancel it out on both sides of the equation. This leaves us with:
P_g = RT/V

Finally, we can plug in the values for R, T, and V to get our answer:
P_g = (96 ft-lb/lb R)(80 F)(10 ft^3/lbm) = 7680 ft-lb/ft^3

However, we want our answer in units of pressure (psi or psig), so we need to convert ft-lb/ft^3 to psi. To