# Calc AB Related Rates Problem

## 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

$\frac{P}{T}$ = constant

## The Attempt at a Solution

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

T$\frac{dP}{dT}$ - P$\frac{dT}{dT}$ = 0

So solving for dP/dt:

$\frac{dP}{dt}$ = $\frac{P}{T}$$\frac{dT}{dt}$

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?

Mark44
Mentor

## 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.
15°C per minute is not a temperature. It's the time rate of change of temperature. What is the exact wording of this problem?
What is the rate of change of the pressure inside the container at time t=0?

## Homework Equations

$\frac{P}{T}$ = constant

## The Attempt at a Solution

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

T$\frac{dP}{dT}$ - P$\frac{dT}{dT}$ = 0

So solving for dP/dt:

$\frac{dP}{dt}$ = $\frac{P}{T}$$\frac{dT}{dt}$

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?

That is the exact wording of the problem. That's why I said the wording was odd.

Mark44
Mentor
Whoever wrote the problem made a mistake. I would get some clarification from the instructor as to what the real problem is.

That's what I expected, thank you!