A house has well insulated walls. It contains a vol of 100m^3 of air at 300K
a) calculate the E required to increase the T of the diatomic gas by 1.00C
b) If this E could be used to lift an object of mass m through a height of 2.00m what is the mass of m?
Oh..I got a humongous number drwls.
I used PV=nRT
T= 274.15K
P= 1atm
V=100m^3
R= 8.2x10^-5 m^3* atm / K*mol
then I got 4,448.33mol
then I plugged that into
Q= nCp(DeltaT)
Cp= 7/2*R
T= 274.15K
n=4,448.33mol
Q= 35469438.74 J ?!
Why is it so bib
a) Even thought the volume is known, this will not be a constant-volume heating of the gas. Some will expand through cracks around windows and doors, and through the chimney, if there is one. It is a constant-pressure heating, and the specific heat for a diatomic molecule in such a process is 7R/2. I don't have my calculagtor wth me, but that's about 7 Calories per mole degC. Use the perfect gas law and the volume to get the number of moles of gas in the house. Multiply by 4.18 if you want the energy in Joules.
b) Set the heat energy required (in J) equal to m g H, with H = 2 m. Solve for M.
Thanks very much drwls =)
I have a question about the pressure ..what do I use if it's not given?
do I just use 1atm ?
Assume 1 atmosphere, about 1.02*10^5 N/m^2
To calculate the energy required to increase the temperature of the diatomic gas by 1.00°C, you can use the formula:
E = m * c * ΔT,
where E is the energy required, m is the mass of the gas, c is the specific heat capacity of the gas, and ΔT is the change in temperature.
a) To calculate the energy (E) required:
1. Find the mass (m) of the gas. The volume of air is given as 100 m^3. However, we need to know the density of the gas in order to find the mass. Without the density, we cannot determine the mass.
2. Determine the specific heat capacity (c) of the gas. The specific heat capacity depends on the type of diatomic gas. Without this information, we cannot proceed with the calculation.
Therefore, without the density and specific heat capacity values, we cannot determine the exact energy required.
b) It is not possible to determine the mass (m) of an object that can be lifted using the energy calculated in part a without additional information. The energy required to lift an object through a height is given by:
E = m * g * h,
where E is the energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height.
In this case, you only have the energy (E) calculated in part a, but you need either the mass (m), acceleration due to gravity (g), or height (h) to determine the remaining unknown variable. Without any of this information, the mass of the object cannot be determined.