If given the ratio of temperatures in Celsius to Kelvin for Gold to silver as 1.10614 to 1.08265. How can I find the temperatures of each individual element form just this information?
A Celsius temperature is always lower than a Kelvin temperature, at the same temperature. For example, 100 C = 373 K.
So how can the ratio of T(C) to T(K) be greater than 1?
It is unclear if your ratios are T(C)/T(K) or T(gold)/T(silver) using a given scale.
Make sure you are stating the problem correctly
After a little checking, I believe the question is meant to be:
"If given the ratios of melting points of Gold and silver are 1.10614 in Celsius, and 1.08265 in Kelvin. How can I find the melting points of each individual element from just this information?"
Let
S=melting point of silver in Celsius, and
G=melting point of gold in Celsius, then
G/S = 1.10614
(G+273.15)/(S+273.15)=1.08265
Cross multiply each equation and solve for G and S.
G=1.10614S...(1)
G+273.15=1.08265(S+273.15)...(2)
Eliminate G by subtracting (2) from (1)
(1.10614-1.08265)S=(1.08265-1)273.15
S=22.576/0.02349
=961.08 °C
G=1.10614*961.08
=1063.09°C
To find the temperatures of gold and silver individually, we can set up a system of equations using the given ratio of temperatures.
Let's assume that the temperature of gold in Celsius is represented by "x" and the temperature of silver in Celsius is represented by "y".
Since the given ratio states that the temperature of gold to silver in Celsius to Kelvin is 1.10614 to 1.08265, we can set up the following equation:
x / y = 1.10614 / 1.08265
Now, to convert the temperatures from Celsius to Kelvin, we need to add 273.15 to each temperature. Let's call the converted temperatures of gold and silver in Kelvin "a" and "b", respectively.
So the equations become:
x + 273.15 = a
y + 273.15 = b
Now we have a system of three equations:
x / y = 1.10614 / 1.08265
x + 273.15 = a
y + 273.15 = b
To solve this system of equations, you can use various methods such as substitution, elimination, or matrices.
By substituting the second and third equations into the first equation, you can solve for "x" and "y". After finding the values of "x" and "y", you can calculate the corresponding temperatures in Kelvin by substituting them into the second and third equations, respectively.
Once you have solved the equations, you will obtain the temperatures of gold and silver in Celsius and Kelvin.