# Calculate uncertainty in pressure, temperature and time?

• TheNovice11
In summary, after conducting a lab on air compressors and calculating error in pressure, temperature, and time measurements, the values of n were found to be 1.01347534, 1.015041506, 1.015031517, 1.01798942, and 1.019624199. The questions posed were: 1) What type of compression is occurring? 2) Are the values of n equal from each set of data? 3) Do they increase or decrease in chronological order? 4) What is the cause of any differences? And 5) What is the uncertainty in pressure, temperature, and time measurements? In order to determine the uncertainty, the Root Mean Square may
TheNovice11

## Homework Statement

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After doing a lab on air compressors, we were asked to calculate Error in Pressure, Temperature and time measurements taken (all at 30 second intervals). We took pressure and temperature values at time = 0,30,60,90,120,150 and 180 seconds. We repeated the experiment 5 times. Before each repetition, we took atmospheric pressure and temperature. The values of n I calculated using equation 2 were:
1.01347534,
1.015041506
1.015031517
1.01798942
1.019624199
1) What type of compression is occurring (Isothermal, Isentropic or Polytropic)?
2) Are the Values on n equal from each set of data?
3) Do they increase or decrease when placed in chronological order?
4) Explain the cause of any differences?
5)What is the uncertainty in pressure, temperature and time measurements?

## Homework Equations

(P1)(V1)^n = (P2)(V2)^n (1)

n = (ln(Pf/P0))/(ln(Pf/P0)-ln(Tf/T0)) (2)

## The Attempt at a Solution

My attempt at a solution is partly explained under the 'problem statement' section. However, I have found that we also probably need to use the Root Mean Square to calculate the uncertainty in each of our values, by manipulating Equation 1 possibly? I also included questions 1-4 as maybe they are needed to answer question 5. I will be on this forum constantly to clarify anything. Thank you

For the uncertainties in the measured values you'll have to check the measurement apparatus and the way you got your values. I would avoid using the 5 different data points for an estimate as they will probably overestimate your measurement error (can you guarantee that the compression was done in exactly the same way every time?).

Equation (2) will help to propagate the uncertainties to an uncertainty of n.

## 1. How do you calculate uncertainty in pressure?

To calculate uncertainty in pressure, you need to have measured values for pressure and the corresponding uncertainties for each measurement. Then, you can use the formula: uncertainty in pressure = (maximum pressure - minimum pressure) / 2. This will give you the range of possible values for pressure, taking into account the uncertainties.

## 2. What factors contribute to uncertainty in temperature measurements?

There are several factors that can contribute to uncertainty in temperature measurements, including the precision and accuracy of the measurement device, variations in the environment or conditions under which the measurement is taken, and human error in reading or recording the temperature.

## 3. Can uncertainty in time affect the accuracy of a measurement?

Yes, uncertainty in time can affect the accuracy of a measurement. This is because time is often a factor in other measurements, such as velocity or rate, and any uncertainty in the time measurement will also contribute to the overall uncertainty in those measurements.

## 4. How can you minimize uncertainty in pressure, temperature, and time measurements?

To minimize uncertainty in these measurements, it is important to use high-quality and precise measurement devices, ensure that the measurements are taken in controlled and consistent conditions, and repeat the measurements multiple times to account for any variations or errors.

## 5. What is the significance of calculating uncertainty in scientific measurements?

Calculating uncertainty in scientific measurements is important because it allows us to understand the limitations of our data and the potential for errors or variations in our measurements. It also helps to ensure the accuracy and reliability of our results and conclusions by accounting for any uncertainties.

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