Adiabatic compression of an ideal gas

[Rasine]

An ideal gas at a temperature of 17.7°C is compressed adiabatically from an initial volume 70.0 l to a final volume 43.0 l. Find its final temperature (in °C) if CV = 2.50R.


so T1V1^g=T2V2^g


to find g=cp/cv=(cv+nR)/cv and cv=2.50R

g=(2.50R+nR)/2.50R factor out an R g=(2.50+n)/2.50 factor out 2.50

g=n/2.50

but how do i find n...if what i did above is even right

 

[Andrew Mason]

An ideal gas at a temperature of 17.7°C is compressed adiabatically from an initial volume 70.0 l to a final volume 43.0 l. Find its final temperature (in °C) if CV = 2.50R. so T1V1^g=T2V2^g

It helps to start with the correct relationship. The adiabatic condition is:

$$PV^\gamma = K$$

Substitute P = nRT/V to give:

$$TV^{\gamma-1} = K/nR = constant$$

You can't determine what n is since you don't have the pressure. But you don't need it to solve the question.

AM

 

[Rasine]

so how do i get what i denoted as g

 

[Rasine]

do i solve for what ever nR is

 

[Rasine]

i am so confused! please give me another hint

 

[Andrew Mason]

i am so confused! please give me another hint

What is $TV^{\gamma-1}$ initially?

Does it change?

So what is it at the end?

You are given the volume at the end. So what is T at the end?

Note: $\gamma = C_p/C_v \text{ and } C_p = C_v + R$

$\gamma$ is simply a ratio of specific heats so it is dimensionless.

AM