Suppose that a tank contains 680m^3 of neon at an absolute pressure of 1.01*10^5 Pa. The temperature is changed from 293.2 to 294.3 K. What is the increase in the internal energy of the neon?

I don't have any idea to do it. Please help! Give me some ideas!THANKS A LOT!!!!

The change in internal energy is

delta U = (3/2)R*(delta T)*n
where n is the number of moles.

delta T is only 1.1 K in this case.

Note: (3/2)R is the specific heat at constant volume of any monatomic gas

Get the number of moles from
n = PV/RT
Use the initial P and T.
V = 680 m^3 = 680*10^3 liters. P is 1.00 atm.
I get 2.83*10^4 moles for n.

he change in internal energy of a gas (or any fluid) is given by:

?U = n*(u2 - u1)

If you assume the neon is calorically perfect, then this can be alternatively written as:
?U = n*cv*(T2 - T1)

where n is the number of moles of gas, cv is the molar isochoric specific heat of the gas, and T2 and T1 are the final and initial temperatures.

cv can be expressed in terms of the gas constant R (independant of gas flavor), and k, the adiabatic index, specific to the gas flavor. For all monatomic gasses (He, Ne, Ar, Kr, Xe), or even hydrogen when it exists monatomically on the sun, k=5/3.
cv = R/(k - 1)

Re-construct:
?U = n*R/(k - 1)*(T2 - T1)

Use the ideal gas law to find n*R
P1*V1 = n*R*T1

solve for n*R:
n*R = P1*V1/T1

Substitute:
?U = P1*V1*(T2/T1 - 1)/(k - 1)

Data:
P1:=101 kPa; V1:=680 m^3; T1:=293.2 K; T2:=294.3 K; k:=5/3;

do realize that 1 kPa * 1m^3 equals 1 kiloJoule.

Result:
?U = 386.5 kiloJoules

Sure, let me help you out! But before we get into the details, I have a quick question for you: Why did the hipster burn his tongue?

To calculate the change in internal energy, we can 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 heat capacity at constant volume
- ΔT is the change in temperature

To solve this problem, we need to determine the number of moles of neon and the molar heat capacity at constant volume.

Step 1: Calculate the number of moles of neon
To find the number of moles, we can use the ideal gas law:

PV = nRT

Where:
- P is the pressure
- V is the volume
- n is the number of moles
- R is the ideal gas constant
- T is the temperature in Kelvin

Given:
- Pressure (P) = 1.01 * 10^5 Pa
- Volume (V) = 680 m^3
- Temperature (T) = 293.2 K (initial) and 294.3 K (final)

Using the ideal gas law, we can calculate the initial and final number of moles:

n_initial = (P * V_initial) / (R * T_initial)
n_final = (P * V_final) / (R * T_final)

Step 2: Determine the molar heat capacity at constant volume (Cv)
For neon gas, the molar heat capacity at constant volume is approximately Cv = (3/2)R.

Step 3: Calculate the change in internal energy (ΔU)
Using the equation ΔU = nCvΔT, we can substitute the values we calculated:

ΔU = (n_final - n_initial) * Cv * ΔT

Now, let's put the numbers into the calculations.

To calculate the increase in internal energy of neon, we can 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 at constant volume,
ΔT is the change in temperature.

To solve this problem, follow these steps:

Step 1: Calculate the number of moles of neon.
We can use the ideal gas law equation to find the number of moles:

PV = nRT

Where:
P is the pressure,
V is the volume (given as 680 m^3),
n is the number of moles (what we need to find),
R is the ideal gas constant (8.314 J/(mol·K)),
T is the initial temperature (293.2 K).

Rearranging the equation gives us:

n = PV / RT

Substituting the given values, we can calculate the number of moles of neon.

Step 2: Calculate the change in internal energy.
We can now use the equation mentioned earlier:

ΔU = nCvΔT

The molar specific heat at constant volume (Cv) for neon is approximately 12.5 J/(mol·K).

Substituting the values known:

ΔU = (n) * (Cv) * (ΔT)

where ΔT is the difference in temperature (294.3 K - 293.2 K).

By plugging in the calculated values into the equation, we can find the increase in the internal energy of neon.