1000cm *3 of air at 20 degree celicius&101.35kpa is heated at constant pressure until volume doubles, find find temperature&work?
work= P*(Vf-Vi)
tempfinal= 2*tempinitial (in Kelvins).
To find the final temperature and work done, we can use the ideal gas law and the formula for work done in a gas expansion or compression.
1. Convert the given volume: 1000 cm^3 to m^3.
1 m^3 = 1000000 cm^3
1000 cm^3 * (1 m^3 / 1000000 cm^3) = 0.001 m^3
2. Convert the given pressure: 101.35 kpa to Pascals.
1 kPa = 1000 Pa
101.35 kPa * (1000 Pa / 1 kPa) = 101350 Pa
Now, let's calculate the final temperature using the ideal gas law:
PV = nRT
Where:
P = pressure
V = volume
n = amount of substance (in moles)
R = ideal gas constant (8.314 J/(mol·K))
T = temperature
We need to find the final temperature, so we rearrange the equation:
T = PV / nR
However, since the mass or moles of air is not given, we can cancel out the amount of substance by assuming that the number of moles is constant throughout the process.
Now, let's find the final temperature:
T = (101350 Pa * 0.001 m^3) / (1 mol * 8.314 J/(mol·K))
Simplifying the equation:
T = 12219.2 K
The final temperature is approximately 12219.2 Kelvin.
Next, let's calculate the work done during the process.
The work done on the gas during an expansion or compression can be calculated using the following formula:
Work = PΔV
Where:
P = constant pressure
ΔV = change in volume
In this case, the volume doubles, so the change in volume (ΔV) is:
ΔV = 2 * initial volume - initial volume
= 2 * 0.001 m^3 - 0.001 m^3
= 0.001 m^3
Now, let's calculate the work done:
Work = (101350 Pa) * (0.001 m^3)
= 101.35 J
The work done during the process is approximately 101.35 Joules.