A gas at 273 kelvin expands by 0.1 cubic metre if it is heated through 50 kelvin. Calculate the original volume at constant pressure
To solve this problem, we can use the formula for thermal expansion:
ΔV = V₀ * α * ΔT
Where:
ΔV is the change in volume
V₀ is the original volume
α is the coefficient of volume expansion
ΔT is the change in temperature
We need to find the original volume, so let's rearrange the formula to solve for V₀:
V₀ = ΔV / (α * ΔT)
In this case, we have:
ΔV = 0.1 m³
ΔT = 50 K
The coefficient of volume expansion for gases is approximately constant and given by α = 1/273 K⁻¹. In this case, the initial temperature is 273 K, so the change in temperature is 50 K.
Plugging in the values, we have:
V₀ = 0.1 m³ / ( (1/273 K⁻¹) * 50 K )
Simplifying this equation, we can multiply the numerator and denominator by 273 K⁻¹ to get:
V₀ = 0.1 m³ * ( 273 K / 50 )
V₀ = 0.1 m³ * 5.46
V₀ = 0.546 m³
Therefore, the original volume of the gas at constant pressure is 0.546 cubic meters.