Related Rates: Calculating the Pressure Change in a Gas Container

[pry_or]

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]

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?

 

[pry_or]

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

 

[Mark44]

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

 

[pry_or]

That's what I expected, thank you!