# Thermodynamic question

1. Dec 12, 2008

### Shayna

1. The problem statement, all variables and given/known data
A rigid container holds 0.680 g of hydrogen gas. How much heat is needed to change the temperature of the gas
From 50 K to 100 K?
From 250 K to 300 K?
From 550 K to 600 K?
From 2250 K to 2300 K?

3. The attempt at a solution
I calculated the first one using delta E_th = (3/2)N*K_b*delta T
= (0.68g/2.0158g/mol)*6.02*10^23*1.38*10^-23*50K=210J

I don't understand why there should be a difference the questions, it seems to me all the temperature difference is 50K

2. Dec 12, 2008

### Andrew Mason

If you use the ideal gas law, there is no difference to the answers. If you use the actual heat capacities of H2 gas, however, the heat capacity increases with temperature. See this chart for example. (Use: $Q = mC_v\Delta T$). If you are using the ideal gas law, you have to use a molar heat capacity for Cv = 5R/2 since H2 gas is diatomic.

AM

Last edited: Dec 12, 2008
3. Dec 12, 2008

### Shayna

For example From 250 K to 300 K
I got the Cv from the form =14.55 therefore Cp=Cv+R=22.84
LaTeX Code: Q = mC_v\\Delta T =0.68*10^-3 kg * 22.84* 50K = 776.56 J
But that isn't right

4. Dec 12, 2008

### Andrew Mason

Why are you using Cp? If Q = mC_v\\Delta T and Cv = 14.55, why are you using a heat capacity of 22.84? Is pressure constant in this process?

AM