Determine initial and final temperatures, adiabatic expansion?

[snowicorn]

Homework Statement

A 3.25 mol sample of an ideal diatomic gas expands adiabatically from a volume of 0.1050 m^3 to 0.762 m^3. Initially the pressure was 1.00 atm

Determine the initial and final temperatures

Homework Equations

PV^γ= nRT

The Attempt at a Solution

To get the initial temperature, I used the above equation

*note: converted atm to N/m^2

T = PV^γ/nR = (1.013 *10^5 N/m^2)((0.1050 m^3)^1.4)/ (3.25 mol * 8.314 J/mol*K)

T = 159.8 K

Unfortunately that isn't the correct answer and the correct answer is actually 394 K. I'm pretty sure I'm going through the steps correctly. But no matter how I put the above into the calculator, I keep getting the wrong answer.

All help is appreciated! :)

 

[ehild]

Homework Statement

A 3.25 mol sample of an ideal diatomic gas expands adiabatically from a volume of 0.1050 m^3 to 0.762 m^3. Initially the pressure was 1.00 atm

Determine the initial and final temperatures

Homework Equations

PV^γ= nRT

The Attempt at a Solution

To get the initial temperature, I used the above equation

*note: converted atm to N/m^2

T = PV^γ/nR = (1.013 *10^5 N/m^2)((0.1050 m^3)^1.4)/ (3.25 mol * 8.314 J/mol*K)

T = 159.8 K

Unfortunately that isn't the correct answer and the correct answer is actually 394 K. I'm pretty sure I'm going through the steps correctly. But no matter how I put the above into the calculator, I keep getting the wrong answer.

All help is appreciated! :)

The equation marked with red is wrong.
PV=nRT for an ideal gas. And pV^γ= const during an adiabatic process.

ehild

 

[sankalpmittal]

Homework Statement

A 3.25 mol sample of an ideal diatomic gas expands adiabatically from a volume of 0.1050 m^3 to 0.762 m^3. Initially the pressure was 1.00 atm

Determine the initial and final temperatures

Homework Equations

PV^γ= nRT

The Attempt at a Solution

To get the initial temperature, I used the above equation

*note: converted atm to N/m^2

T = PV^γ/nR = (1.013 *10^5 N/m^2)((0.1050 m^3)^1.4)/ (3.25 mol * 8.314 J/mol*K)

T = 159.8 K

Unfortunately that isn't the correct answer and the correct answer is actually 394 K. I'm pretty sure I'm going through the steps correctly. But no matter how I put the above into the calculator, I keep getting the wrong answer.

All help is appreciated! :)

You should first use P₁V₁^γ = P₂V₂^γ to evaluate for final pressure of the gas.

And , PV^γ= nRT is wrong ! Its PV^γ=constant. Also it will be correct to write PV=nRT...

Hint : What is γ for diatomic gas ?