Physics help, Regarding Ideal gas?

Question

If a certain sample of monoatomic ideal gas has pressure of 100kPa. What is internal energy of 1m³ of gas.

Assume nothing except atoms of ideal gas do not interact and obey Newtonian mechanincs.

Please, people, do not use Maxwell distribution, and the like. The real solution is only three lines long and invololves no integration (at least expicitly).

.
Kenny,

what is n,
what is R,
and what is T?

And where did you get your equation?

Answer 1

Do it with dimensional analysis. Internal energy has units of pressure times volume, so if an ideal gas has a pressure of 100,000 N/m² or J/m³, then anything energy inside of it is 100,000 Nm per m³ or Joules per m³. Am I close? Nah, there's a factor of 3/2 here, internal energy should be 150,000 J/m³. Let's see....

Okay, consider balls of mass m going in one direction, so that they have momentum mx/t (m = mass, x = length, t = time). Pressure is change in momentum per area per unit time, or (mx/t)(1/x²)(1/t), or m/xt². But energy is (1/2)mx²/t², which divided by volume x³ gets you (1/2)m/xt². Since there are 3 component axes of momenta, we increase this by a factor of 3 to get (3/2)m/xt².

Answer 2

initiate with pV = n RT the place n = style of moles. you comprehend p, R, and T and you extremely need Na*n/V - that supply you molecules/volume. So. n/V = p/(RT) multiply the two factors by way of Na Na*n/V = p*Na/(RT) enable Na*n/V = N = numbre of molecules/ m^3. Then to get moelcules/cm^3, multiply by way of 10^-6 N (molecule/cm^3) = 10^-6 (m/cm^3) p*Na/(RT) plug interior the numbers and make advantageous you convert C to Kelvin by way of including 273.

Answer 3

PV=nRT

T=PV/nR