The temperature, T, of a given mass of gas varies inversely with its volume, V. The temperature of 20 cm3 of a certain gas is 15°C. What will the temperature be when it is compressed to a volume of 5 cm3?
• 10°C
• 300°C
• 6.67°C
• 60°C
How?
since TV = k is constant,
T(5) = (15)(20)
In the real world, T is usually in Kelvin degrees.
What was the answer?
To solve this problem, we need to understand the concept of inverse variation and use the equation that relates temperature and volume.
In inverse variation, two variables are related in such a way that when one variable increases, the other variable decreases, and vice versa. The equation for inverse variation is written as:
T = k/V
where T represents the temperature, V represents the volume, and k is a constant of proportionality.
We are given that the temperature, T, is 15°C when the volume, V, is 20 cm3. Let's use this information to find the value of k.
15 = k/20
To find k, we can rearrange the equation:
k = 15 * 20
k = 300
Now we have the value of k as 300.
Next, we need to find the temperature when the volume is 5 cm3. Let's substitute the values into the equation:
T = 300/5
T = 60°C
So, the temperature is 60°C when the volume is 5 cm3.
Therefore, the correct answer is 60°C.