# Ideal gas law and temperature

1. Jan 16, 2009

### shehry1

1. The problem statement, all variables and given/known data
This is Pathria (2nd Ed) 1.6 and it seemed simple enough but the magnitude of the answer seems unbelievably large:

A cylindrical vessel 1 m long and .1 m in diameter is filled with a monoatomic gas at P = 1 atm and T = 300 K. The gas is heated by an electrical discharge along the axis of the vessel, which releases an energy of 10^4 joules. What will the temperature of the gas be immediately after the discharge.

2. Relevant equations
PV = nRT
E = 3nRT/2

3. The attempt at a solution
E2 - E1 = 10^4
nR = P1 * V/T1 where P1 = 1 and T1 = 300
V = pi * (.1/2)^2 * 1

E2 - E1 = (3/2)(nR)(T2 - T1)
10^4 = (3/2) (1 * V) (T2 - 300)/300

This seems to give an answer in the range of 10^8. Is this correct? Is it because the number of moles of the gas PV/RT are very few and that even this 'normal' increase in energy is leading to such epic temperatures. The magnitude is bothersome especially because even the sun's core is at a temperature of the order of 10^6

2. Jan 16, 2009

### Staff: Mentor

Check your units. Pay special attention to pressure.

3. Jan 16, 2009

### D H

Staff Emeritus
... and to the gas constant R.

4. Jan 16, 2009

### Staff: Mentor

There is no R in the final equation

5. Jan 16, 2009

### Andrew Mason

This is correct. You have to be clearer in your reasoning. Isolate T2, find nR and V and plug in the numbers.

Another way of approaching this is to work out the heat capacity of the gas nCV. Since the volume does not change, the change in temperature is just the added heat energy divided by the heat capacity:

$$nC_v = \frac{3}{2}nR = \frac{3PV}{2T} = 3\times 100325\times 7.85\times 10^{-3}/2 \times 300 = 3.93 J/K$$

$$T_2 = \Delta E/nC_v + T_1$$

AM

6. Jan 16, 2009

### D H

Staff Emeritus
Point taken. What Borek was talking about in post #2 is this:
shehry1, you are being very sloppy with units here (there are no units here!) That's a freshman mistake. From your other posts (Jackson, spin matrices, theoretical mechanics), you are not a freshman.