Problem-1 A manufacturer has provided you with a solid, right cylindrical mass of aluminum. The specifications indicate that the cylinder has a radius of 2.5cm and a length of 1.5cm at a reference temperature of To=22C and that the aluminum used has a coefficient of linear expansion of 25 x 10-6/C. Based on these specifications, what is the maximum percent uncertainty in the volume of the cylinder at the reference -temperature? m² +80 V = πrah = 3.14 x (2.5) 2+1.5 V- 29. 4375 10 °C 2 C 5cm ±0.1 am n + 01 m 1 besla
Kinetic Theory of Gas
The Kinetic Theory of gases is a classical model of gases, according to which gases are composed of molecules/particles that are in random motion. While undergoing this random motion, kinetic energy in molecules can assume random velocity across all directions. It also says that the constituent particles/molecules undergo elastic collision, which means that the total kinetic energy remains constant before and after the collision. The average kinetic energy of the particles also determines the pressure of the gas.
P-V Diagram
A P-V diagram is a very important tool of the branch of physics known as thermodynamics, which is used to analyze the working and hence the efficiency of thermodynamic engines. As the name suggests, it is used to measure the changes in pressure (P) and volume (V) corresponding to the thermodynamic system under study. The P-V diagram is used as an indicator diagram to control the given thermodynamic system.
To calculate the uncertainty in the volume.
Given:
The radius of the cylinder:
The length of the cylinder is:
To calculate:
The percentage uncertainty of the volume:
When two or more quantities are multiplied, their relative uncertainties get added to obtain the relative uncertainty of the answer.
If:
Then:
When a quantity is multiplied by an exact number, the uncertainty also gets multiplied by that number.
The percentage uncertainty of a quantity is given by:
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