Two moles of helium gas initially at 213 K
and 0.17 atm are compressed isothermally ton1.19 atm. Find the final volume of the gas. Assume that helium behaves as an ideal gas. The universal gas constant is 8.31451 J/K · mol. Answer in units of m3
Part 2
Find the work done by the gas. Answer in units of kJ.
Part 3
Find the thermal energy transferred. Answer in units of kJ.
To find the final volume of the helium gas, 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 gas constant, and T is the temperature in Kelvin.
First, let's convert the temperatures to Kelvin:
Initial temperature (T1) = 213 K
Final temperature (T2) = 213 K (isothermal process)
Given:
Initial pressure (P1) = 0.17 atm
Final pressure (P2) = 1.19 atm
Number of moles (n) = 2 moles
Gas constant (R) = 8.31451 J/K·mol
Using the ideal gas law equation and rearranging it to solve for V2 (final volume):
V2 = (P1 * V1 * T2) / (P2 * T1)
Now let's plug in the values:
V1 is not given, but since the process is isothermal (constant temperature), we know that the initial volume (V1) is equal to the final volume (V2). Therefore, we can leave it as V for simplicity.
V = (P1 * V * T2) / (P2 * T1)
Substituting the given values:
V = (0.17 atm * V * 213 K) / (1.19 atm * 213 K)
Canceling out the units:
V = V * (0.17 / 1.19)
Simplifying the expression:
1 = 0.17 / 1.19
Therefore, we can conclude that the final volume V will be equal to the initial volume V.
Now let's move on to Part 2 to find the work done by the gas.
The work done in an isothermal process is given by the equation:
W = -nRT * ln(P2 / P1)
Using the given values,
W = -2 mol * 8.31451 J/K·mol * ln(1.19 / 0.17)
Calculating the value of ln(1.19 / 0.17) ≈ 1.826
W = -2 mol * 8.31451 J/K·mol * 1.826
Finally, let's move on to Part 3 to find the thermal energy transferred.
The thermal energy transferred in an isothermal process is equal to the work done by the gas. Therefore,
Thermal energy transferred = -W
Substituting the calculated value of W from Part 2, we get:
Thermal energy transferred = -(-2 mol * 8.31451 J/K·mol * 1.826)
After calculating the expression, you will get the answer in units of kJ.