# First Law of Thermodynamics and temperature

Gee Wiz

## Homework Statement

A toy balloon is initially at a temperature of T = 20°C. Its initial volume is 0.0042 m3 (It is a 10 cm radius sphere). Assume that the pressure in the balloon always equals atmospheric pressure, 101.3 kPa.
The new temp was found to be 52.23°C
By how many Joules did the internal energy of the gas in the balloon increase? Air is almost entirely diatomic gas.
ΔU =?

T*N*α*K
pv=rnt
pv=kNt

## The Attempt at a Solution

5/2*(52.23-20)*1.381e-23*N

n=pv/rt
N=n*6.022e23

I keep getting 1.17e-4, and it says i am off by a power of 10. I am not sure where I am messing up

barryj
What is your equation for change in internal energy. I am trying to work this problem but I get a much different answer so I am probably using the wrong equation.

What did you get for n, the number of moles?

Last edited:
Homework Helper

## Homework Statement

A toy balloon is initially at a temperature of T = 20°C. Its initial volume is 0.0042 m3 (It is a 10 cm radius sphere). Assume that the pressure in the balloon always equals atmospheric pressure, 101.3 kPa.
The new temp was found to be 52.23°C
By how many Joules did the internal energy of the gas in the balloon increase? Air is almost entirely diatomic gas.
ΔU =?

T*N*α*K
pv=rnt
pv=kNt

## The Attempt at a Solution

5/2*(52.23-20)*1.381e-23*N

n=pv/rt
N=n*6.022e23

I keep getting 1.17e-4, and it says i am off by a power of 10. I am not sure where I am messing up

What did you get for N?

ehild

Gee Wiz
it is the degrees of freedom (5/2 for diatomic)*(Temperature)*(K which is a constant 1.381e-23)*(# of molecules)

barryj
So, what did you get for N or n?

Gee Wiz
n= 1.746e-7
N=1.05e17

barryj
I think your value for n is incorrect. Did you get it from the equation

PV = nRT

?

Gee Wiz
Yes. I did 1*.0042e-3/(.08206*293)..converting the kPa's to atms and Celsius to k

barryj
Using PV = nRT I have always used P in Pascals, V in meters^3 n in moles R = 8.32 and T = 293.

If you use P in atm, then is the constant 0.082 correct?

Gee Wiz
yes i think so

barryj
My previous post is incorrect. I should have said the volume is in liters, not meter^3

Gee Wiz
right, and I think that m^3=mL=.001L

barryj
So when I change my calculation from m^3 to liters I get an answer closer to yours but not exact.

so, to find n, we use pressure in Pascals, volume in liters, R = 8.3, and K = 293.
so what do you get for n?

Gee Wiz
1.74e-4

barryj
I agree. Now, change in internal energy is (5/2)Rn(delta T)?

Gee Wiz
I believe so

barryj
I get (5/2)(8.31)(1.74E-4)(32.2) = I can't give the answer

Gee Wiz
I get the same message with that answer that I do with my previous one. "It appears you have made a power of ten error"

Gold Member
In PV = nRT, [P] = N/m2, [n] = mol, [T] = K and with R = 8.31, [R] = J K-1mol-1 => [V] = J m2/N = m3, no?

barryj
Are you using Quest? sometimes their answers are wrong. I get .116 if I use the equation above or if I use your original equation. I think you made a math error when you got 1.17 E-4.

Gee Wiz
I am not 100% sure about your units for P and V (it may just be notation i am not familiar with)
I usually see [P]=atm or pascals, [V]=L (m^3=mL)

Gee Wiz
It's smart physics

barryj
I think we agree on n = -1.74E-4, the units of p and v are done with.

This means that N = (1.74E-4)(6.022E23) =1.04E20

1.17E-4 is not correct didn't you get .117?

Gee Wiz
Here is everything I am doing

=(5/2)*(1.381e-23)*(32.23)*( (1*.0042)/(.08206*293) )* (6.022e23)

barryj
I don't recognize some of your constants and conversions but.....

Take your equation from post #1, 5/2*(52.23-20)*1.381e-23*N and plug in the value for N

N = (1.74E-4)(6.02E23) = 1.04E20 and what do you get? .116 or .117 I think this is the correct answer.

Check your math and we will agree even though smart Physics says we are off. I don't believe it.

Gee Wiz
I get .117

barryj
.117 is not what you reported in post #1. I think .117 is correct.

Mentor
1m^3 is 1000 liters. So the balloon volume is 4.2 liters. From the ideal gas law, the number of gram moles n = 0.175. So ΔU=2.5nRΔT=1.156 liter-atm. How many Joules is that?

Gee Wiz
Ahh, I see my mistake. I was using from units for the volume. Thank you! I got the correct answer now. I appreciate everyone's help

barryj
I feel like an idiot :-(

Homework Helper
Why do you not use SI units? And you do not need to evaluate n or N.

PV=nRT. ΔU=5/2 (nR) ΔT. -->

nR=PV/T , ΔU=2.5 PV ΔT/T.

P=101.3 kPa=1.013 e5 Pa. V=4.2 e-3 m3. T=293 K, ΔT=32.23 K.

The result is in joules.