When a monoatomic ideal gas expand at a constant temperature 200000pa the volume of the gas increases by .005.determine how much heat energy flows into and out the gas
To determine the amount of heat energy flowing into or out of a gas during expansion, we need to use the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the heat supplied to the system minus the work done by the system.
Given:
Pressure (P) = 200,000 Pa
Change in volume (ΔV) = 0.005 m³
Temperature (T) = constant
To calculate the amount of heat energy, we need the equation for the change in internal energy, ΔU:
ΔU = Q - W
Where:
ΔU = Change in internal energy
Q = Heat transferred to/from the system
W = Work done by the system
Since the temperature remains constant (isothermal process), we can use the ideal gas equation to relate pressure, volume, and temperature:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Gas constant
T = Temperature
Since it is a monoatomic ideal gas, the number of moles (n) remains constant.
Rearranging the equation, we get:
PΔV = nRT
We can substitute the given values and solve for n:
(200,000 Pa)(0.005 m³) = n(8.314 J/mol·K)(T)
n = (200,000 Pa)(0.005 m³) / (8.314 J/mol·K)(T)
Now we can calculate the work done by the gas during expansion using the formula:
W = PΔV
W = (200,000 Pa)(0.005 m³)
Once we know the work done, we can use it to determine the heat transfer (Q) from the first law equation:
ΔU = Q - W
Since the temperature remains constant, there is no change in internal energy (ΔU = 0), so we can rewrite the equation as:
Q = W
Now we can plug in the calculated value for work (W) to find the heat transfer (Q).