Charles law
If the relationship between temperature and volume of a gas at a constant pressure is linear, explain why the volume of a gas doesn’t double when its temperature doubles from 10.0°C to 20.0°C.
The T Charles' law talks about is kelvin and not celsius.
So 283.1 to 293.1 is nowhere near doubling.
To understand why the volume of a gas doesn't double when its temperature doubles, we need to refer to Charles' Law. Charles' Law states that the volume of a gas is directly proportional to its temperature, provided the pressure and amount of gas remain constant. In equation form, it can be expressed as:
V₁ / T₁ = V₂ / T₂
where V₁ and V₂ are the volumes of the gas at temperatures T₁ and T₂, respectively.
Now, let's calculate the volume of a gas at two different temperatures, 10.0°C and 20.0°C. Let's assume the initial volume of the gas at 10.0°C is V₁.
Using Charles' Law equation, we can write:
V₁ / 10.0 = V₂ / 20.0
To determine why the volume doesn't double when the temperature doubles, we can compare the values of V₁ and V₂. We can rearrange the equation for V₂:
V₂ = (V₁ / 10.0) * 20.0
From this equation, we can observe that V₂ will be equal to V₁ if and only if the initial temperature, T₁, is 0°C (because 0/10 * 20 = 0). In all other cases, V₂ will be less than V₁.
Therefore, the volume of a gas does not double when its temperature doubles because Charles' Law demonstrates that the relationship between volume and temperature is not a direct proportion at non-zero temperatures.