A container of volume 0.71 m3

contains 1 mol
of argon gas at 27◦C.
Assuming argon behaves as an ideal gas,
find the total internal energy of this gas. The
value of gas constant is 8.31451 J/mol · K

.

Answer: The total internal energy of the gas is 2,092.9 J.

To find the total internal energy of the gas, we can use the formula:

Total Internal Energy = (3/2) * R * T * n

Where:
R = gas constant (8.31451 J/mol · K)
T = temperature (in Kelvin)
n = number of moles of gas

Given:
Volume of container = 0.71 m3
Number of moles of argon gas = 1 mol
Temperature = 27°C = 27 + 273.15 = 300.15 K

Substituting the values into the formula:

Total Internal Energy = (3/2) * 8.31451 J/mol · K * 300.15 K * 1 mol

Calculating:

Total Internal Energy = (3/2) * 8.31451 J/mol · K * 300.15 K * 1 mol
= 3735.759 J

Therefore, the total internal energy of the gas is 3735.759 J.

To find the total internal energy of the argon gas, we need to use the ideal gas law and the formula for internal energy.

The ideal gas law equation is: PV = nRT

Where:
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles of the gas,
R is the gas constant, and
T is the temperature of the gas in Kelvin.

First, we need to convert the temperature from Celsius to Kelvin. Celsius can be converted to Kelvin by adding 273.15. So, 27°C + 273.15 = 300.15 K.

Given:
V = 0.71 m^3
n = 1 mol
T = 300.15 K
R = 8.31451 J/mol · K

We can rearrange the ideal gas law equation to solve for P:
P = nRT / V

Substituting the given values, we get:
P = (1 mol) * (8.31451 J/mol · K) * (300.15 K) / (0.71 m^3)

Now, calculate the pressure:
P = 8.31451 * 300.15 / 0.71 = 3498.57 Pa

Since we know the pressure, volume, and number of moles of the gas, we can calculate the internal energy using the formula:

Internal Energy = (3/2) * n * R * T

Substituting the values:
Internal Energy = (3/2) * (1 mol) * (8.31451 J/mol · K) * (300.15 K)

Now, calculate the internal energy:
Internal Energy = 3/2 * 8.31451 * 300.15 = 3734.706 J

Therefore, the total internal energy of the argon gas is approximately 3734.706 J.