Answer:
To determine the factor by which the volume of a substance must be increased when the temperature is increased from 25oC to 50oC, we need to know the substance's coefficient of thermal expansion.
The coefficient of thermal expansion is a measure of how much a substance's volume will increase in response to a given temperature change.
Assuming that we have the coefficient of thermal expansion for the substance in question, we can use the following formula to calculate the factor by which the volume must be increased:
Factor = 1 + coefficient of thermal expansion * (change in temperature)
In this case, the change in temperature is 50oC - 25oC = 25oC. Therefore, the factor by which the volume must be increased is:
Factor = 1 + coefficient of thermal expansion * 25oC
The exact value of the factor will depend on the substance's coefficient of thermal expansion. In general, substances with a high coefficient of thermal expansion will have a larger increase in volume when the temperature is increased.