Solution Found!
A balloonist is preparing to make a trip in a
Chapter 5, Problem 60P(choose chapter or problem)
A balloonist is preparing to make a trip in a helium-filled balloon. The trip begins in early morning at a temperature of \(15^{\circ} \mathrm{C}\). By midafternoon, the temperature has increased to \(30^{\circ} \mathrm{C}\). Assuming the pressure remains constant at 1.00 atm, for each mole of helium, calculate:
The initial and final volumes
The change in internal energy,
The work (w) done by the helium (in J)
The heat (q) transferred (in J)
Explain the relationship between the answers to (d) and (e).
Equation Transcription:
15°C
30°C
E
Text Transcription:
15°C
30°C
Delta E
E=3/2nRT
Questions & Answers
QUESTION:
A balloonist is preparing to make a trip in a helium-filled balloon. The trip begins in early morning at a temperature of \(15^{\circ} \mathrm{C}\). By midafternoon, the temperature has increased to \(30^{\circ} \mathrm{C}\). Assuming the pressure remains constant at 1.00 atm, for each mole of helium, calculate:
The initial and final volumes
The change in internal energy,
The work (w) done by the helium (in J)
The heat (q) transferred (in J)
Explain the relationship between the answers to (d) and (e).
Equation Transcription:
15°C
30°C
E
Text Transcription:
15°C
30°C
Delta E
E=3/2nRT
ANSWER:
Solution 60P:
Step 1: (a)
Here, we are going to calculate the initial and final volume of the gas.
For initial volume (Vinitial)
Given that,
Pressure, P =1.0 atm
Gas constant, R =0.0821 atm.L.mol-1K-1
Moles, n=1.0 mol
Temperature, T =15°C =273.15 +15 =288.15 K
We know from the ideal gas equation,
=
=
=23.657 L
Thus, the initial volume of He gas is 23.66 L.