# Adiabatic process

Gyroscope

## Homework Statement

3.14
(0.5) How is the fractional change in temperature related to $$\frac{dT}{T}$$ the fractional change in pressure $$\frac{dP}{P}$$ ?
(IPhO 2006)

## Homework Equations

$$PV^{\gamma}=\rm constant$$

## The Attempt at a Solution

nC_vdT=-PdV (1), dV/dP=-nRT/(P^2)

If I substitute dV in the equation (1) it does not give the right result.

Can someone help me, please? :tongue2:

Thanks my dear friends.

## Answers and Replies

marcusl
Science Advisor
Gold Member
It appears you are talking about an ideal gas? Then in
$$P=nRT/V$$
we see right away that P changes the same way as T. This is shown mathematically as

$$\frac{dP}{dT}=\frac{nR}{V},$$

$$\frac{dP}{P}=\frac{nRdT}{PV}=\frac{dT}{T}.$$

Gyroscope
Thanks marcusl for your help. But you are wrong. :( I already solved it. Thanks anyway my dear friend.

marcusl
Science Advisor
Gold Member
Sorry! Glad you solved it.