Answer:
Therefore, when the cake batter containing 5000 bubbles is baked at 170°C, there will be an increase in volume of approximately 353 mL. and look at the explaination.
Step-by-step explanation:
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Calculation of Volume Increase in Baked Cake
To calculate the increase in volume when the cake is baked, we can use the ideal gas law, which states that the volume of a gas is directly proportional to its temperature, assuming constant pressure. The ideal gas law is given by the equation:
1
/
1
=
2
/
2
Where:
1
= initial volume of the gas
1
= initial temperature of the gas
2
= final volume of the gas
2
= final temperature of the gas
Given that the average volume of each bubble in the cake batter is 0.15 mL at 28°C and there are 5000 bubbles, we can calculate the initial total volume of the bubbles:
Initial total volume (
1
) = Average volume of one bubble Number of bubbles `
1
=
0.15
5000
=
750
`
The initial temperature (
1
) is 28°C, and the final temperature (
2
) is 170°C. We need to convert these temperatures to Kelvin by adding 273.15 to each Celsius temperature:
1
(
)
=
28
+
273.15
=
301.15
2
(
)
=
170
+
273.15
=
443.15
Now we can use the ideal gas law to find the final volume (
2
):
1
/
1
=
2
/
2
2
=
(
1
*
2
)
/
1
2
=
(
750
*
443.15
)
/
301.15
2
≈
1103
Therefore, the increase in volume when the cake is baked is approximately:
Increase in volume = Final volume - Initial total volume Increase in volume ≈ 1103 mL - 750 mL Increase in volume ≈ 353 mL
Therefore, when the cake batter containing 5000 bubbles is baked at 170°C, there will be an increase in volume of approximately 353 mL.
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