Final answer:
To find the new volume of a CO₂ bubble in cake batter when heated from 27°C to 177°C, we use Charles's Law. Converting temperatures to Kelvin and plugging into the formula V1/T1 = V2/T2, we can solve for the new volume.
Step-by-step explanation:
A student asked about the change in the volume of a CO₂ bubble in cake batter when heated from 27°C to 177°C.
To calculate the new volume of the bubble, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature, provided the pressure and amount of gas remain constant.
The formula for this is V1/T1 = V2/T2, where V1 is the initial volume, T1 is the initial temperature in Kelvin, V2 is the final volume, and T2 is the final temperature in Kelvin.
To solve for V2, we first need to convert the temperatures from Celsius to Kelvin by adding 273.15.
The initial temperature (T1) in Kelvin is 27°C + 273.15 = 300.15 K, and the final temperature (T2) is 177°C + 273.15 = 450.15 K.
Plugging these values into the equation along with the initial volume (V1) of 0.20 mL, we get:
0.20 mL / 300.15 K = V2 / 450.15 K
Multiplying both sides by 450.15 K, we get:
V2 = (0.20 mL × 450.15 K) / 300.15 K
=0.2999
new volume of the CO₂ bubble in the batter once heated.