Question

Perfectly rigid containers each hold n moles of ideal gas, one being ∇ Part A hydrogen (H

2
​
) and other being neon (Ne). If it takes 300 J of heat to increase the temperature of the hydrogen by 3.30
∘
C, by how many degrees will the same amount of heat raise the temperature of the neon? Express your answer in degrees Celsius.

Answer 1

To find the change in temperature for neon when the same amount of heat is added as in the case of hydrogen, you can use the equation for heat capacity and the given values.

Step-by-step explanation:

The heat capacity of neon (Ne) can be calculated using the equation:

(3/2)nR = 2²/xR

Since the volume of the vessel remains constant, the change in temperature for neon can be calculated as:

Change in temperature for neon = (Heat for hydrogen x Heat capacity of neon) / Heat capacity of hydrogen

Substituting the given values:

Change in temperature for neon = (300 J x (2² / x 8.314)) / ((3/2) x 8.314)

Calculate the value to find the change in temperature for neon.

Answer 2

Using the specific heat capacities of hydrogen and neon, we can calculate that the same amount of heat will raise the temperature of neon by 5.5 ℃.

Step-by-step explanation:

To determine by how many degrees the same amount of heat will raise the temperature of neon, we need to know the specific heat capacities of hydrogen and neon. Hydrogen (H2) is a diatomic molecule, while neon (Ne) is a monatomic noble gas. The specific heat capacity at constant volume (Cv) for a monatomic ideal gas is 3/2 R, where R is the universal gas constant (8.314 J/mol·K). For a diatomic ideal gas like hydrogen, Cv is 5/2 R. Given that it takes 300 J of heat to raise the temperature of hydrogen by 3.30 ℃, we can set up a proportion to find the temperature change for neon using its respective specific heat capacity.

For hydrogen: q = n Cv ΔT

For neon: q = n Cv ΔT (with a different Cv value for monatomic gas)

Using the proportion based on the heat capacity ratio and the known temperature change of hydrogen, we can now calculate the temperature change for neon:

ΔTNe = ΔTH2 × (Cv,H2 / Cv,Ne) = 3.30 ℃ × (5/2 R / 3/2 R) = 5.5 ℃

So, the same amount of heat will raise the temperature of the neon by 5.5 ℃.