Suppose a tank contains 714 m3 of neon (Ne) at an absolute pressure of 1.01×10^5 Pa. The temperature is changed from 293.2 to 294.7 K. What is the increase in the internal energy of the neon?

To calculate the increase in the internal energy of neon, we need to use the equation:

ΔU = nCvΔT

Where:
ΔU is the change in internal energy,
n is the number of moles of neon,
Cv is the molar specific heat capacity at constant volume for neon, and
ΔT is the change in temperature.

To find the number of moles of neon (n), we can use the ideal gas law equation:

PV = nRT

Where:
P is the absolute pressure of the gas,
V is the volume of the gas,
n is the number of moles of the gas,
R is the ideal gas constant (8.314 J/(mol·K)), and
T is the temperature of the gas in Kelvin.

In this case, we know the absolute pressure (P) is 1.01×10^5 Pa and the volume (V) is 714 m3.

Let's calculate the number of moles of neon first:

n = PV / RT

Where:
R = 8.314 J/(mol·K)

Convert the volume from m3 to liters (L):

V = 714 m3 = 714000 L

We also need to convert the temperature from Celsius to Kelvin:

Initial temperature (T1) = 293.2 K
Final temperature (T2) = 294.7 K

Now, we can calculate the number of moles (n) using the ideal gas law:

n = (P * V) / (R * T1)

Next, we need to find the molar specific heat capacity at constant volume for neon (Cv). For monoatomic gases like neon, Cv is given as 3/2 R.

Finally, we can calculate the change in internal energy (ΔU) using the formula:

ΔU = n * Cv * ΔT

Substitute the values into the equation to find the increase in the internal energy of the neon.