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The pressure P, temperature T, and volume V of one mole of
Chapter 3, Problem 8E(choose chapter or problem)
The pressure \(P\), temperature \(T\), and volume \(V\) of one mole of an ideal gas are related by the equation PV = 8.31T , when \(P\) is measured in kilopascals, \(T\) is measured in kelvins, and \(V\) is measured in liters.
a. Assume that \(P=242.52\pm0.03\mathrm{\ kPa}\) and \(V=10.103\pm0.002\mathrm{\ L}\). Estimate \(T\), and find the uncertainty in the estimate.
b. Assume that \(P=242.52\pm0.03\mathrm{\ kPa}\) and \(T=290.11\pm0.02\mathrm{\ K}\). Estimate \(V\), and find the uncertainty in the estimate.
c. Assume that \(V=10.103\pm0.002\mathrm{\ L}\) and \(T=290.11\pm0.02\mathrm{\ K}\). Estimate \(P\), and find the uncertainty in the estimate.
Equation Transcription:
Text Transcription:
P
T
V
P = 242.52 pm 0.03 kPa
V = 10.103 pm 0.002 L
T = 290.11 pm 0.02 K
Questions & Answers
QUESTION:
The pressure \(P\), temperature \(T\), and volume \(V\) of one mole of an ideal gas are related by the equation PV = 8.31T , when \(P\) is measured in kilopascals, \(T\) is measured in kelvins, and \(V\) is measured in liters.
a. Assume that \(P=242.52\pm0.03\mathrm{\ kPa}\) and \(V=10.103\pm0.002\mathrm{\ L}\). Estimate \(T\), and find the uncertainty in the estimate.
b. Assume that \(P=242.52\pm0.03\mathrm{\ kPa}\) and \(T=290.11\pm0.02\mathrm{\ K}\). Estimate \(V\), and find the uncertainty in the estimate.
c. Assume that \(V=10.103\pm0.002\mathrm{\ L}\) and \(T=290.11\pm0.02\mathrm{\ K}\). Estimate \(P\), and find the uncertainty in the estimate.
Equation Transcription:
Text Transcription:
P
T
V
P = 242.52 pm 0.03 kPa
V = 10.103 pm 0.002 L
T = 290.11 pm 0.02 K
ANSWER:Solution 8E
Step1 of 4:
We have Pressure = P, Temperature = T, Volume = V.
One mole of an ideal gas are related by the equation PV = 8.31T.
Here pressure p is measured in kilopascals, T is measured in Kelvins, and V is measured in liters.
Here is our goal is:
a).We need to estimate T, and find the uncertainty in the estimate by assuming that P = 242.52 ± 0.03 kPa and V = 10.103 d = 0.002 L.
b).We need to estimate V, and find the uncertainty in the estimate by assuming that
P = 242.52 ± 0.03 kPa and T = 290.11 ± 0.02 K.
c).We need to Estimate P, and find the uncertainty in the estimate by assuming that V = 10.103 ± 0.002 L and T = 290.11 ± 0.02 K.
Step2 of 4:
a).
From the given information we have P = 242.52, , V = 10.103 and d = 0.002L.
We have PV = 8.31T
Then,
T =
=
=
= 294.8471.
Hence, T = 294.8471.
Consider,
T =
Differentiate above equation with respect to “P” then
=
= (1)
Substitute V value in above equation we get
=
= 1.2157
Hence, = 1.2157.
Again consider,
T =
Differentiate above equation with respect to “V” then
=
= (1)
Substitute P value in above equation we get
=