Consider a piece of metal that is at 5 deg C. If it is heated until it has twice the internal energy, its temperature will be.
a)556 deg C
b)283 deg C
c)273 deg C
d)278 deg C
e)10 deg C
Thermal E~kT, where k is the Boltzmann constant, T is the temperature in Kelvins
5℃=278K
Answ. 278 x 2=556 K
Would the answer be B because the temperatures are denoted in deg C? 556K - 273 = 283 deg C.
To determine the temperature after the metal is heated and has twice the internal energy, we can use the formula for the change in internal energy:
ΔU = mCΔT
Where:
ΔU represents the change in internal energy
m represents the mass of the metal
C represents the specific heat capacity of the metal
ΔT represents the change in temperature
Since the metal is the same, its mass remains constant, so we can simplify the equation to:
ΔU = CΔT
If the metal is heated until it has twice the internal energy, we can write this as:
2U = CΔT
Rearranging the equation to solve for ΔT gives us:
ΔT = 2U / C
We know that the initial temperature of the metal is 5°C, but we don't know the specific heat capacity of the metal. Therefore, we cannot calculate the exact temperature. The options provided do not include the specific heat capacity of the metal, so we cannot determine the correct answer.
To answer this question, we need to understand the relationship between internal energy and temperature. The internal energy of an object is directly proportional to its temperature.
The equation that relates internal energy (U) and temperature (T) is given by:
U = mcΔT
Where:
U is the internal energy
m is the mass of the object
c is the specific heat capacity of the object
ΔT is the change in temperature
In this case, we have a piece of metal with an initial temperature of 5°C. We need to determine the final temperature when the internal energy is doubled.
Let's assume that the mass and specific heat capacity of the metal remain constant.
Let's denote the initial internal energy and temperature as U1 and T1, respectively. Similarly, the final internal energy and temperature as U2 and T2, respectively.
Given that U2 = 2U1 (twice the initial internal energy), we can rewrite the equation as:
2U1 = mcΔT
Since we are asked to find the final temperature, we need to eliminate U from the equation and rearrange it:
2U1 = mc(T2 - T1)
Dividing both sides of the equation by mc, we get:
2 = (T2 - T1)
Now, substitute T1 = 5°C:
2 = (T2 - 5)
Solve for T2:
T2 = 2 + 5
T2 = 7°C
Therefore, the final temperature of the metal when its internal energy is twice the initial value is 7°C.
Since none of the answer choices provided matches 7°C, it seems like there might be an error in the given options.