Change in enthalpy and change in internal energy are state functions. The value of `DeltaH, DeltaU` can be determined by using Kirchoff's equation.
Calculate `DeltaH` when `10dm^(3)` of helium at NTP is heated in a cylinder to `100^(@)C`, assuming that the gas behave ideally.

Options

A. 927.9J
B. 279.2J
C. 729.3J
D. 999J

Answer

To calculate the change in enthalpy (ΔH) when heating 10 dm³ of helium at normal temperature and pressure (NTP) to 100°C, we can follow these steps:

### Step 1: Determine the number of moles of helium (N)
At NTP, the molar volume of an ideal gas is approximately 22.4 dm³/mol.

\[ N = \frac{\text{Volume}}{\text{Molar Volume}} = \frac{10 \, \text{dm}^3}{22.4 \, \text{dm}^3/\text{mol}} \approx 0.4464 \, \text{mol} \]

### Step 2: Calculate the heat capacity at constant pressure (Cₚ)
For a monoatomic ideal gas like helium, the specific heat at constant volume (Cᵥ) is given by:

\[ Cᵥ = \frac{3}{2} R \]

Where R is the universal gas constant (8.314 J/(mol·K)). Therefore,

\[ Cᵥ = \frac{3}{2} \times 8.314 \approx 12.471 \, \text{J/(mol·K)} \]

Now, using the relation \(Cₚ = Cᵥ + R\):

\[ Cₚ = Cᵥ + R = \frac{3}{2} R + R = \frac{5}{2} R \]

Calculating \(Cₚ\):

\[ Cₚ = \frac{5}{2} \times 8.314 \approx 20.785 \, \text{J/(mol·K)} \]

### Step 3: Calculate the change in temperature (ΔT)
The initial temperature (T₁) is 0°C (or 273.15 K) and the final temperature (T₂) is 100°C (or 373.15 K).

\[ \Delta T = T₂ - T₁ = 373.15 \, \text{K} - 273.15 \, \text{K} = 100 \, \text{K} \]

### Step 4: Calculate the change in enthalpy (ΔH)
Using the formula for enthalpy change:

\[ \Delta H = N \cdot Cₚ \cdot \Delta T \]

Substituting the values we calculated:

\[ \Delta H = 0.4464 \, \text{mol} \cdot 20.785 \, \text{J/(mol·K)} \cdot 100 \, \text{K} \]

Calculating ΔH:

\[ \Delta H \approx 0.4464 \cdot 20.785 \cdot 100 \approx 927.90 \, \text{J} \]

### Final Answer:
The change in enthalpy (ΔH) when heating 10 dm³ of helium to 100°C is approximately **927.90 J**.

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