A monoatomic gas expands isobarically.What will be the percentage of heat supplied that increases the thermal energy and that involved in doing work for expansion?
The first law of thermodynamics
ΔQ =ΔU + W.
The work done by system is
W = p•ΔV =ν•R•ΔT.
The change in internal energy is
ΔU = ν•(i/2) •R•ΔT,
where the degrees of freedom i = 3,
ΔQ =ΔU + W = ν•(i/2) •R•ΔT + ν•R•ΔT = =2.5 •ν•R•ΔT,
ΔU/ ΔQ = ν•(i/2) •R•ΔT /2.5 •ν•R•ΔT =3/5 = 0.6.
60%
W/ ΔQ = ν•R•ΔT/2.5 •ν•R•ΔT = 0.4
40%
To determine the percentage of heat supplied that increases the thermal energy (q+), and the percentage of heat involved in doing work for expansion (w), we need to understand the concepts of specific heat at constant pressure (Cp) and the first law of thermodynamics.
1. Calculate the change in thermal energy (ΔE):
The change in thermal energy (ΔE) can be calculated using the equation:
ΔE = q+ - w
where q+ represents the heat added to the system, and w represents the work done by the system.
2. Since the gas is expanding isobarically (at constant pressure):
For an isobaric process, the work done (w) can be calculated using the equation:
w = PΔV
where P is the constant pressure and ΔV is the change in volume.
3. Determine the heat supplied (q+):
The heat supplied (q+) can be determined using the equation:
q+ = ΔE + w
4. Calculate the percentage of heat supplied that increases thermal energy:
To determine the percentage of heat supplied that increases thermal energy (%q+), use the equation:
%q+ = (q+ / ΔE) * 100
5. Calculate the percentage of heat involved in doing work for expansion:
To determine the percentage of heat involved in doing work for expansion (%w), use the equation:
%w = (w / q+) * 100
By following these steps, you can calculate the percentage of heat supplied that increases the thermal energy, and the percentage of heat involved in doing work for expansion for the given scenario.