An ideal gas is compressed at constant pressure to one-half its initial volume. If the pressure of the gas is 120 kPa, and 760 J of work is done on it, find the initial volume of the gas.
To find the initial volume of the gas, we can use the relationship between work done, pressure, and volume.
According to the formula for work done on a gas at constant pressure, the work done (W) is given by the equation: W = PΔV, where P is the pressure and ΔV is the change in volume.
Given that the pressure of the gas is 120 kPa and the work done on the gas is 760 J, we can substitute these values into the formula to obtain:
760 J = (120 kPa) * ΔV
To isolate ΔV, we need to convert the pressure from kPa to Pa:
120 kPa = 120,000 Pa
Now we can rearrange the equation:
760 J = (120,000 Pa) * ΔV
Next, we can solve for ΔV:
ΔV = 760 J / (120,000 Pa)
Simplifying the expression:
ΔV = 0.00633 m^3
Since the gas is compressed to one-half its initial volume, the change in volume is equal to half of the initial volume:
ΔV = (1/2) * V_i
Substituting the value of ΔV, we can solve for the initial volume (V_i):
0.00633 m^3 = (1/2) * V_i
Now we can isolate V_i by multiplying both sides by 2:
V_i = 2 * 0.00633 m^3
V_i = 0.01266 m^3
Therefore, the initial volume of the gas is 0.01266 m^3.
To find the initial volume of the gas, we can use the formula for work done on a gas at constant pressure:
Work = Pressure * Change in Volume
Given that the pressure of the gas is 120 kPa and 760 J of work is done on it, we can write the equation as:
760 J = 120 kPa * Change in Volume
To find the change in volume, we rearrange the equation:
Change in Volume = 760 J / 120 kPa
Convert kPa to Pa:
1 kPa = 1000 Pa
Change in Volume = 760 J / (120 kPa * 1000 Pa/kPa)
Change in Volume = 0.00633 m^3
Since the gas is compressed to one-half its initial volume, we can find the initial volume by doubling the change in volume:
Initial Volume = 2 * 0.00633 m^3
Initial Volume = 0.01266 m^3
Therefore, the initial volume of the gas is 0.01266 m^3.