Using the ideal gas law with two unknowns

In summary, the given problem involves a closed container with a single atom ideal gas at volume V1= 0,45*10^(-3) m^3, pressure p1 = 3,2 MPa, and temperature T1 = 892 K. The volume of the gas is then increased to V2 = 8*V1 and the goal is to find the resulting pressure and temperature. Using the ideal gas equation, p = (nRT)/V, and the fact that the expansion is adiabatic, we can manipulate the equation to solve for pressure. However, there is still uncertainty in finding the new temperature, as the given equation T2 = T1*(V1/V2)^(γ
  • #1
kaffekjele
20
0

Homework Statement



You are given a closed container containing a single atom ideal gas.
The volume is V1= 0,45*10^(-3) m^3
Pressure p1 is 3,2 MPa
Temperature, T1, is 892 K

The volume of the gas is increased to V2= 8*V1

Find the pressure and temperature after the increase of volume.


Homework Equations



Ideal gas equation pV=nRT





The Attempt at a Solution



I have n= 0,19 moles from a previous question. R is the ideal gas constant, 8,31 J/moles*K

Manipulating the ideal gas equation for pressure gives me p = (nRT)/V but that leaves T as an unknown so I'm not sure if that's the right way to go...
 
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  • #2
I would expect that the expansion is adiabatic, this gives another constraint on the gas.
 
  • #3
I was looking at that and tried to find the new temperature by using T2= T1*([itex]\frac{V1}{V2}[/itex])[itex]\gamma-1[/itex] which gave me 221,46K which is not correct according to my lecturer.
 
  • #4
It would be interesting to see how the lecturer would solve this.
 
  • #5
kaffekjele said:
I was looking at that and tried to find the new temperature by using T2= T1*([itex]\frac{V1}{V2}[/itex])[itex]\gamma-1[/itex] which gave me 221,46K which is not correct according to my lecturer.

I get 223 K. What does your lecturer think about that answer?
 

FAQ: Using the ideal gas law with two unknowns

What is the ideal gas law and how is it used?

The ideal gas law is a mathematical formula that describes the relationship between pressure, volume, temperature, and the number of moles of a gas. It is commonly written as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. This law is used to calculate the values of any of the variables if the other three are known.

What are the units used in the ideal gas law?

The units used in the ideal gas law depend on the values of the variables being calculated. In most cases, pressure is measured in atmospheres (atm), volume in liters (L), temperature in Kelvin (K), and the number of moles is unitless. However, it is important to ensure that all units are consistent when plugging values into the equation.

What is the difference between two unknowns in the ideal gas law and one unknown?

The ideal gas law can be used to calculate the value of one variable if the other three are known. However, in some cases, there may be two unknown variables that need to be solved for. This requires an additional equation or piece of information to be able to solve for both unknowns. For example, if two gases are mixed together, the total pressure and total volume can be used to solve for the individual pressures or volumes of each gas using the ideal gas law.

Can the ideal gas law be used for all gases?

The ideal gas law is most accurate for gases at low pressures and high temperatures. At high pressures, the volume of the gas molecules becomes significant and at low temperatures, intermolecular forces between molecules become significant. As a result, the ideal gas law is less accurate for gases under these conditions and other equations, such as the van der Waals equation, should be used.

What are some real-world applications of using the ideal gas law with two unknowns?

The ideal gas law is commonly used in many industries, such as in the production of chemicals and in the design of engines. In these applications, the gas law is used to calculate the optimal conditions for reactions or to understand the behavior of gases in different environments. The use of the ideal gas law with two unknowns allows for more precise calculations and can aid in the design and optimization of various processes.

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