One mole of an ideal gas initially at a temperature of Ti = 7.4°C undergoes an expansion at a constant pressure of 1.00 atm to eight times its original volume.
(a) Calculate the new temperature Tf of the gas.______J
(b) Calculate the work done on the gas during the expansion.________kJ
Good response, just remember to have a negative sign in the work if asking for work done on the gas.
(a)
Ti=273+7.4=280.4 K
Vi/Ti = Vf/Tf
Vi/280.4 =8 Vi/Tf
Tf=8•280.4 = 2243.2 K
b) p•ΔV=νRΔT
ν =1 mol
p•ΔV= RΔT
W = p•ΔV= RΔT=
= 8.31•(2243.2-280.4)=
=1.63•10⁴ J =16.3 kJ
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(a) Well, you know what they say, when a mole of gas expands at a constant pressure, the temperature starts to cool down faster than an ice cream in the Sahara desert! To find the new temperature, we can use the good old equation:
Tf = Ti(Vf/Vi)
Now you just need to plug in the values and let the math do its magic. Good luck!
(b) Ah, the work done on the gas during expansion. It's like getting a high-five from a ghost, you can't really feel it, but you know it's there. To calculate the work done, you can use the equation:
Work = P(Vf - Vi)
Just remember to convert the pressure from atm to Joules, and the volume from moles to kilojoules. Happy math-ing!
To calculate the new temperature and work done on the gas, we can use the ideal gas law and the first law of thermodynamics.
(a) To find the new temperature Tf of the gas, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L * atm / (K * mol))
T = temperature (in Kelvin)
First, let's convert the initial temperature from Celsius to Kelvin:
Ti = 7.4°C + 273.15 = 280.55 K
Now, let's solve for Tf. Since the pressure and number of moles of gas are constant, we have the equation:
(P * V) / T = constant
Since the volume is being increased by a factor of 8, we can write:
(P * 8V) / Tf = (P * V) / Ti
Simplifying the equation, we get:
8 / Tf = 1 / Ti
Now, let's isolate Tf:
Tf = (8 * Ti) / 1
Substituting the values, we have:
Tf = (8 * 280.55) K
Tf = 2244.4 K
Therefore, the new temperature Tf of the gas is 2244.4 K.
(b) To calculate the work done on the gas during the expansion, we can use the formula:
Work = -P * ΔV
Where:
P = constant pressure (1.00 atm)
ΔV = change in volume (final volume - initial volume)
The initial volume is V and the final volume is 8V. Therefore, the change in volume is:
ΔV = 8V - V
ΔV = 7V
Substituting the values, we have:
Work = -(1.00 atm) * (7V)
Now, we need to convert the work from liters * atm to kilojoules (kJ). The conversion factor is:
1 L * atm = 101.3 J
1 kJ = 1000 J
So, to convert the units of work, we divide by 101.3 J and then multiply by 1000 to get kJ:
Work = (-(1.00 atm) * (7V) / 101.3 J) * (1000 kJ / 1 J)
Now, the work done on the gas is:
Work = -68.97 * V kJ
Therefore, the work done on the gas during the expansion is -68.97 times the initial volume of the gas, in kilojoules.