A piece of iron has a temperature of 0 zero degrees Celsius. At what temperature would the iron atoms have twice as much kinetic energy?
K.E. = (3/2)*k*T, where k is the Boltzman constant.
You must always take temperature in Kelvin, so the given temperature is 273K
=> (K.E.1) = (3/2)*k(273)
=> (K.E.2) = 2(K.E.1) = 2*(3/2)*k*(273)
= (3/2)*k*(2*273)
= (3/2)*k*(546)
The new temperature is double the old, since temperature and K.E. are directly proportional. The required temp. is 546K, or 273 degrees Celsius.
To determine at what temperature the iron atoms would have twice as much kinetic energy, we can use the equation for kinetic energy:
KE = (1/2)mv^2
Where KE is the kinetic energy, m is the mass, and v is the velocity of the atoms. However, in this case, we are interested in comparing the kinetic energy at two different temperatures.
The kinetic energy of particles is directly proportional to their temperature, according to the kinetic theory of gases. The temperature is also directly proportional to the average kinetic energy of the particles.
Therefore, if we want the iron atoms to have twice the kinetic energy, we need to find the temperature at which the average kinetic energy is doubled.
Let's assume that the average kinetic energy of the iron atoms at 0 degrees Celsius is KE1. So, we have:
KE1 = (1/2)mv^2
Now, let's find the temperature at which the average kinetic energy is doubled, which we will call T2.
To find T2, we can use the formula:
KE2 = 2 * KE1
Since kinetic energy is directly proportional to temperature, we have:
T2 / T1 = 2
Now, let T1 be the temperature in degrees Celsius and T1 + 273 be the temperature in Kelvin.
(T2 + 273) / (T1 + 273) = 2
Cross-multiplying, we get:
T2 + 273 = 2 * (T1 + 273)
T2 + 273 = 2T1 + 546
T2 = 2T1 + 546 - 273
T2 = 2T1 + 273
So, the temperature at which the iron atoms would have twice as much kinetic energy is 2 times the initial temperature in degrees Celsius plus 273.
To determine the temperature at which the iron atoms would have twice as much kinetic energy, we need to understand the relationship between temperature and kinetic energy.
The kinetic energy of an object is directly proportional to its temperature. According to the kinetic theory of gases, the average kinetic energy of the particles in a substance is directly proportional to its absolute temperature.
The relationship between kinetic energy (KE) and temperature (T) can be expressed mathematically using the following equation:
KE ∝ T
Here, the symbol "∝" represents "proportional to." This equation implies that if we double the temperature, we also double the kinetic energy.
Now, let's consider the specific scenario of the iron atoms reaching twice their initial kinetic energy. Suppose the initial temperature of the iron is 0 degrees Celsius. However, to calculate the final temperature, we will need to convert it to the Kelvin temperature scale. The Kelvin scale is an absolute temperature scale where 0 K represents absolute zero.
To convert Celsius to Kelvin, we add 273.15 to the Celsius temperature:
0 + 273.15 = 273.15 K
So, the initial temperature of the iron in Kelvin is 273.15 K.
To find the temperature at which the iron atoms would have twice as much kinetic energy, we need to double the initial kinetic energy. Since kinetic energy is directly proportional to temperature, doubling the kinetic energy is equivalent to doubling the temperature.
Therefore, we need to double the initial temperature of the iron in Kelvin:
273.15 K * 2 = 546.3 K
Hence, the temperature at which the iron atoms would have twice as much kinetic energy is approximately 546.3 Kelvin.