Question

A Pyrex measuring cup was calibrated at normal room temperature. How much error will be made in a recipe calling for 410 mL of cool water, if the water and the cup are hot, at 84 ∘C , instead of at room temperature? Neglect the glass expansion.

Answer 1

The error in the recipe will be a decrease of approximately 5.64 mL of water when using a hot Pyrex measuring cup instead of one at room temperature.

Step-by-step explanation:

The error in a recipe calling for 410 mL of cool water, when using a Pyrex measuring cup that is hot at 84°C instead of at room temperature, can be calculated using the principle of thermal expansion. Pyrex has a very small coefficient of linear expansion, so neglecting the glass expansion is a reasonable assumption.

To calculate the error, we can determine the change in volume of the water due to the change in temperature.

The formula for thermal expansion is: ΔV = V₀ * α * ΔT, where ΔV is the change in volume, V₀ is the initial volume, α is the coefficient of linear expansion, and ΔT is the change in temperature.

For water, the coefficient of linear expansion is approximately 0.000212 (1/°C).

Using the formula, we can calculate the change in volume as follows:

1. Convert the given temperatures to Kelvin scale by adding 273.15.
2. The initial temperature is 84°C + 273.15 = 357.15 K, and the room temperature is approximately 298 K.
3. Calculate the change in temperature:
4. ΔT = final temperature - initial temperature
5. = 298 K - 357.15 K
6. = -59.15 K.
7. Calculate the change in volume:
8. ΔV = 410 mL * 0.000212 (1/°C) * (-59.15 K)
9. = -5.64 mL (rounded to two decimal places).

Therefore, the error in the recipe will be a decrease of approximately 5.64 mL of water when using a hot Pyrex measuring cup instead of one at room temperature.