How many times does the internal energy of a tank of gasoline (50 liters) differ from the internal energy

| August 8, 2021 | education

How many times does the internal energy of a tank of gasoline (50 liters) differ from the internal energy of one glass of gasoline (200 cm3) from the same tank? (gasoline density 710 kg / m3)

V1 = 50 l = 50 * 10-3 m3.

V2 = 200 cm3 = 200 * 10-6 m3.

ρ = 710 kg / m3.

U1 / U2 -?

Let us express the internal energy of gasoline U according to the formula of a monoatomic ideal gas: U = 3 * m * R * T / 2, where m is the mass of gasoline, R is the universal gas constant, T is the absolute temperature, M is the molar mass of gasoline.

We express the mass of gasoline m by the formula: m = V * ρ, where V is the volume of gasoline, ρ is the density of gasoline. U1 = 3 * m1 * R * T / 2 = 3 * V1 * ρ * R * T / 2.

U2 = 3 * m2 * R * T / 2 = 3 * V2 * ρ * R * T / 2.

U1 / U2 = 2 * 3 * V1 * ρ * R * T / 2 * 3 * V2 * ρ * R * T = V1 / V2.

U1 / U2 = 50 * 10-3 m3 / 200 * 10-6 m3 = 250.

Answer: the internal energy of a full tank of gasoline is 250 times more than the energy of one glass.



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