# Compressed temperature ?

compressed temperature ???

## Homework Statement

One mole of nitrogen is compressed (by piling lots of sand on the piston) to a volume of 14 liters at room temperature (293 K). The cylinder is placed on an electric heating element whose temperature is maintained at 293.001 K. A quasistatic expansion is carried out at constant temperature by very slowly removing grains of sand from the top of the piston, with the temperature of the gas staying constant at 293 K. (You must assume that there is no energy transfer due to a temperature difference from the gas to the surrounding air, and no friction in the motion of the piston, all of which is pretty unrealistic in the real world! Nevertheless there are processes that can be approximated by a constant-temperature expansion. This problem is an idealization of a real process.) When the volume is 24 liters, how much thermal energy transfer Q has gone from the heating element into the gas?

1. When the volume is 24 liters, how much thermal energy transfer Q has gone from the heating element into the gas?

2. How much work W has been done on the piston by the gas?

3. How much has the energy of the gas changed?

i got number 3. and the answer is 0 J the other two i am completely stuck on.

## The Attempt at a Solution

um... i have no idea where to even start. might just be a simple formula but have been looking in the text book and can not find one. any help would be great!!!!
thanks

## Answers and Replies

I used the equations on page 425 in the book to solve this.
Basically, deltaE = W + Q = 0
so you can say that W = Q
now, you just have to calculate W:

W = -integral(P dV) with your points going from V1 to V2

Substitute in for P
W = -integral( (num of moles * R * T)/V dV) from V1 to V2

so really, you do:
W = -(num moles)*R*T*ln(V1/V2) btw, R = 8.3 J/(K*mole)

ok... i saw that equation but did not know how to cancel out the integral thingy so just assumed that was the wrong equation to use.
thanks and good luck on the final (it should be a fun one lol)

how do you solve for T?