Question

If We Triple The Average Kinetic Energy Of The Gas Atoms, What Is The New Temperature In ∘C?

Answer 1

Tripling the average kinetic energy of gas atoms corresponds to tripling the temperature in Kelvin. After converting the original Celsius temperature to Kelvin, multiplying by three, and converting back, we get the new temperature in Celsius.

Step-by-step explanation:

The average kinetic energy (KE) of gas molecules is directly proportional to their absolute temperature (measured in Kelvin). If we triple the average kinetic energy of the gas atoms, we are in effect tripling the temperature of the gas in Kelvin. To find the new temperature in Celsius, we must convert the original temperature to Kelvin, triple it, and then convert it back to Celsius.

The relationship between average kinetic energy and temperature is given by the equation KE ≈ ½mv² ≈ ¾ kT, where k is Boltzmann's constant, and T is the temperature in Kelvin. Since we are tripling the kinetic energy, we can denote the new temperature as T′ and set up the equation 3KE = ¾ kT′.

To convert the original temperature from Celsius to Kelvin, we add 273.15 to it. If the original temperature is T°C, then in Kelvin, it would be T(K) = T°C + 273.15. To find the new temperature in Celsius after tripling the kinetic energy, we solve T′°C = (T′(K) - 273.15), where T′(K) is 3 times T(K).

For instance, if we start at 20°C, which is 293.15 K, tripling the temperature would give us 879.45 K. Converting back to Celsius, the new temperature would be 606.3°C.

Answer 2

The average kinetic energy of gas atoms is directly proportional to the temperature in Kelvin. A tripling of the average kinetic energy of the gas atoms means that the temperature must also triple. To find the new temperature in °C, triple the initial temperature (converted to Kelvin) and then convert it back to °C by subtracting 273.15.

Step-by-step explanation:

When we talk about the average kinetic energy of gas atoms, we are talking about a principle from thermodynamics, which is part of physics. In general, for an ideal gas, the average kinetic energy of its molecules is directly proportional to the absolute temperature of the gas (in Kelvin).This proportionality is described by the equation:

KE = ½ mv² = (3/2) kT

where KE is the average kinetic energy, m is the mass of the gas molecule, v is the velocity of the gas molecule, k is the Boltzmann constant and T is the absolute temperature in Kelvin.

If we triple the mean kinetic energy (KE) of a gas, this means that the temperature must also triple, since these two quantities are directly proportional by the constant (3/2)k. To convert this new temperature back into degrees Celsius, we need to subtract 273.15 from the new Kelvin temperature.

Let's denote T1 as the initial temperature, KE1 as the initial kinetic energy, T2 as the new temperature, and KE2 as the new kinetic energy:

KE2 = 3 * KE1

T2 = 3 * T1

Convert T1 from °C to K: T1(K) = T1(°C) + 273.15

Calculate T2 in K: T2(K) = 3 * T1(K)

Convert T2 back to °C: T2(°C) = T2(K) - 273.15