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.
You lost me here:
" The experiment is set up when the air pressure is 7 degree Celcius."
To calculate the number of calories added to the flask through heating from the gas burner, we need to determine the change in pressure and the number of moles of air in the flask.
The change in pressure can be calculated using the equation:
ΔP = ρgh
Where:
ΔP is the change in pressure
ρ is the density of the fluid (water)
g is the acceleration due to gravity
h is the difference in height between the two columns of the manometer
In this case, the cap is initially 15 cm above the water column. Let's convert this to meters:
h = 15 cm = 0.15 m
The density of water is approximately 1000 kg/m^3, and the acceleration due to gravity is 9.8 m/s^2. Hence:
ΔP = (1000 kg/m^3)(9.8 m/s^2)(0.15 m)
ΔP = 1470 Pa
Note that 1 atm is equivalent to 101325 Pa. Therefore, the change in pressure is:
ΔP = 1470 Pa - 101325 Pa
ΔP ≈ -100855 Pa
Next, we need to calculate the number of moles of air in the flask. We can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles
R is the ideal gas constant
T is the temperature
The initial pressure (P) is 1 atm, the volume (V) is 1*10^4 m^3, the gas constant (R) is 8.314 J/(mol·K), and the temperature (T) is 7 degrees Celsius. Let's convert the temperature to Kelvin:
T = 7°C + 273.15
T = 280.15 K
Now we can calculate the number of moles:
(1 atm)(1*10^4 m^3) = n(8.314 J/(mol·K))(280.15 K)
n ≈ 3773.6 mol
Finally, we can calculate the amount of heat added to the flask using the specific heat capacity of air:
q = nCΔT
Where:
q is the heat added
n is the number of moles
C is the specific heat capacity
ΔT is the change in temperature
In this case, C is given as 20.8 (J/K)/mol. The change in temperature is the final temperature minus the initial temperature:
ΔT = (7°C + 273.15 K) - 7°C
ΔT = 273.15 K
Calculating the heat added:
q = (3773.6 mol)(20.8 J/K/mol)(273.15 K)
q ≈ 2,366,512 cal
Therefore, approximately 2,366,512 calories have been added to the flask through heating from the gas burner.