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प्रश्न
Express the following physical statements in the form of differential equation.
For a certain substance, the rate of change of vapor pressure P with respect to temperature T is proportional to the vapor pressure and inversely proportional to the square of the temperature
उत्तर
The rate of change of vapor pressure P with respect to time t is `"dP"/"dt"` and the rate of increase vapor pressure is P at time T is proportibnal to the vapor pressure and also is inversely proportional to the square of the temperature is `"dP"/"dt" = "kP"/"T"^2`
Since `"k"/"T"^2 = alpha`
`"dP"/"dt" = alpha`P
⇒ `"dP"/"dt" - alpha"P"` = 0 is a required differential equation.
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