Solve Exponent Question: PV^{\frac{2+f}{f}}

[vorcil]

Ok I mucked up the question

given
$$VT^{\frac{f}{2}$$ = constant
$$T = PV$$
Need help simpi
-------

I get $$V (PV)^{\frac{f}{2}}$$
which is the same as
$$V P^{\frac{f}{2}}V^{\frac{f}{2}}$$
which is the same as
$$P^{\frac{f}{2}} V^{\frac{2+f}{2}}$$

Now how do i simplify it from here?

answer is $$PV^{\frac{2+f}{f}}$$

 

[vorcil]

whoops i Meant

$$PV^{\frac{2+f}{f}}$$ is the answer

 

[vorcil]

Ok I mucked up the question

given
$$VT^{\frac{f}{2}$$ = constant
$$T = PV$$

-------

I get $$V (PV)^{\frac{f}{2}}$$
which is the same as
$$V P^{\frac{f}{2}}V^{\frac{f}{2}}$$
which is the same as
$$P^{\frac{f}{2}} V^{\frac{2+f}{2}}$$

Now how do i simplify it from here?

answer is $$PV^{\frac{2+f}{f}}$$

 

[Mark44]

Ok I mucked up the question

given
$$VT^{\frac{f}{2}$$ = constant
$$T = PV$$

-------

I get $$V (PV)^{\frac{f}{2}}$$
which is the same as
$$V P^{\frac{f}{2}}V^{\frac{f}{2}}$$
which is the same as
$$P^{\frac{f}{2}} V^{\frac{2+f}{2}}$$

Now how do i simplify it from here?

answer is $$PV^{\frac{2+f}{f}}$$

You're given two equations, so any subsequent work should be an equation. Are you trying to solve for one of the variables?

Your second equation seems to be related to the ideal gas law, PV = nRT.

 

[vorcil]

Yeah, I'm trying to understand how to get from

$$ViTi^{\frac{f}{2}}= VfTf^{\frac{f}{2}}== VT^{\frac{f}{2}}$$

To the equivalent equation

$$PV^{\frac{2+f}{f}}$$
using PV=nRT
I just can't seem to figure it out though

 

[Mark44]

Yeah, I'm trying to understand how to get from

$$ViTi^{\frac{f}{2}}= VfTf^{\frac{f}{2}}== VT^{\frac{f}{2}}$$

To the equivalent equation

$$PV^{\frac{2+f}{f}}$$

This is not an equation. An equation states that two expressions have the same value.

using PV=nRT
I just can't seem to figure it out though

What are i and f? My guess is that you are interpreting things incorrectly. For example could what you are writing as Vi be the initial volume? If so, it would be written as V_i. And what you are writing as Vf might be the final volume, V_f. Same with T_i and T_f, which could represent the initial and final temperatures.