- #1

- 9

- 0

## Homework Statement

A container of constant volume contains a quantity of gas under pressure. At t=0, the pressure is 4 psi and the temperature is 15°C per minute. What is the rate of change of the pressure inside the container at time t=0?

## Homework Equations

[itex]\frac{P}{T}[/itex] = constant

## The Attempt at a Solution

Taking the derivative of both sides and then simplifying, I ended up with:

T[itex]\frac{dP}{dT}[/itex] - P[itex]\frac{dT}{dT}[/itex] = 0

So solving for dP/dt:

[itex]\frac{dP}{dt}[/itex] = [itex]\frac{P}{T}[/itex][itex]\frac{dT}{dt}[/itex]

This is where I get stuck. I know P = 4 psi and dT/dt = 15°C per minute, but I can't figure out how to determine T. Without knowing the actual value of the constant in the original formula, I don't see how it is possible. The wording of the temperature value in the problem sounds odd to me. The only thing I can think of is that the temperature should be assumed to be 0°C at t=0 and so dP/dt does not exist. Is this it, or am I missing some way to find T?