An experiment makes use of a water manometer attached to a flask. Initially the two columns in the gas manometer are at the same level and the air pressure in the flask and both sides of manometr is 1 atm. The experiment is set up when the air pressure is 7 degree Celcius. The left side of the manometer is connected to a flask and right side is capped so that the air at the end will be compressed when the flask is heated by a gas burner. The cap is initially 15cm above the water column. The volume of the flask is 1*10^4 m^3. When calculating the change in pressure assosiated with the heating of the gas in the flask, you can neglect the change in the volume of the gas(air in this cae) assosiated with the displacement of the water column in the manometer. Calculate how many calories (cal) have been added to the flask through heating from the gas burner given that specific heat of the air is 20.8 (J/K)/mol.
To calculate the change in pressure associated with the heating of the gas in the flask, you need to use the ideal gas law and the concept of water manometer.
1. Convert the initial temperature from Celsius to Kelvin:
Initial temperature = 7°C + 273.15 = 280.15 K
2. Determine the change in temperature:
Change in temperature = Final temperature - Initial temperature
3. Evaluate the change in pressure using the ideal gas law:
PV = nRT
Since the volume and the number of moles remains constant, we can write the equation as:
P1/T1 = P2/T2
P1 = Initial pressure (1 atm)
T1 = Initial temperature (280.15 K)
T2 = Final temperature
P2 = Calculated final pressure
Rearranging the equation:
P2 = (P1 * T2) / T1
4. Calculate the change in pressure (ΔP):
ΔP = P2 - P1
5. Determine the change in height (Δh) of the water column in the manometer:
Δh = Initial height - Final height
Initial height = 15 cm = 0.15 m
Final height = (initial height) + (change in height) = 0.15 m + Δh
6. Calculate the change in potential energy (ΔPE) of the water column:
ΔPE = (mass of water) * (acceleration due to gravity) * (change in height)
We can neglect the change in volume and assume the density of water remains constant:
mass of water = (density of water) * (volume of water column)
7. Calculate the heat energy (Q) added to the flask using the formula:
Q = ΔPE
Since 1 calorie (cal) = 4.184 Joules (J), convert the value to calories:
Q (cal) = Q (J) / 4.184
8. Calculate the number of moles of air using the ideal gas law:
moles of air = (P1 * V) / (R * T1)
Volume (V) = 1 * 10^(-4) m^3
R = Ideal gas constant = 8.314 J/(mol*K)
9. Finally, calculate the calories added to the flask through heating:
Calories added = (Q (cal) * moles of air) / Avogadro's number
Avogadro's number = 6.022 * 10^23 molecules/mol
10. Substitute the known values into the formulas and calculate the result.
Please note that the specific heat of air is not required for this calculation.