Calculating Heat for Temperature Changes in a Rigid Container | Thermodynamics

[Shayna]

Homework Statement

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?

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

 

[Andrew Mason]

Homework Statement

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?

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

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 http://www.engineeringtoolbox.com/hydrogen-d_976.html" 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

 

[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

 

[Andrew Mason]

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

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