The temperature of a mass of gas (T) varies inversely with volume (V). For a volume of 500 cm^3, the temp is 2.5 degrees Celcius. For a volume of 100 cm^3, what would the temperature be?
12.5 degrees?
you are correct.
An odd formula, as most such calculations are based on degrees Kelvin.
To find the temperature (T) for a given volume (V), we can use the concept of inverse variation. Inverse variation states that when one variable (in this case, temperature) increases, the other variable (in this case, volume) decreases, and vice versa, while their product remains constant.
In this case, we can set up an equation using the given information. Let's denote the initial temperature as T₁ and the initial volume as V₁, and the unknown temperature as T₂ and the unknown volume as V₂. The equation can be written as:
T₁ * V₁ = T₂ * V₂
From the given information, we have:
T₁ = 2.5 degrees Celsius
V₁ = 500 cm^3
We want to find T₂ when V₂ = 100 cm^3.
Plugging in the values into the equation, we have:
2.5 degrees Celsius * 500 cm^3 = T₂ * 100 cm^3
Simplifying the equation:
1250 = T₂ * 100
To find T₂, we can rearrange the equation:
T₂ = 1250 / 100
Solving the equation:
T₂ = 12.5 degrees Celsius
Therefore, for a volume of 100 cm^3, the temperature would be 12.5 degrees Celsius.
So, the answer is 12.5 degrees Celsius, not 12.5 degrees.