You lost me here:
" The experiment is set up when the air pressure is 7 degree Celcius."
" The experiment is set up when the air pressure is 7 degree Celcius."
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.