The following data is given for a ternary \(ABC\) gas mixture at 12 MPa and 308 K:
\(y_i\): mole fraction of component \(i\) in the gas mixture
\(\hat{\phi}_i\): fugacity coefficient of component \(i\) in the gas mixture at 12 MPa and 308 K
The fugacity of the gas mixture is _________ MPa (rounded off to 3 decimal places).
The following data is given for a ternary \(ABC\) gas mixture at 12 MPa and 308 K:
\(y_i\): mole fraction of component \(i\) in the gas mixture
\(\hat{\phi}_i\): fugacity coefficient of component \(i\) in the gas mixture at 12 MPa and 308 K
The fugacity of the gas mixture is _________ MPa (rounded off to 3 decimal places).
Show Hint
Solution and Explanation
Step 1: Calculate the fugacity of each component. For Component \(A\): \(f_A = 0.55 \times 0.75 \times 12 = 4.95 \, {MPa}\) For Component \(B\): \(f_B = 0.20 \times 0.80 \times 12 = 1.92 \, {MPa}\) For Component \(C\): \(f_C = 0.25 \times 0.95 \times 12 = 2.85 \, {MPa}\)
Step 2: Sum the fugacities of all components to find the total fugacity of the mixture. \[ f = f_A + f_B + f_C = 4.95 + 1.92 + 2.85 = 9.72 \, {MPa}\]
Top Questions on Thermodynamics
A hot plate is placed in contact with a cold plate of a different thermal conductivity as shown in the figure. The initial temperature (at time $t = 0$) of the hot plate and cold plate are $T_h$ and $T_c$, respectively. Assume perfect contact between the plates. Which one of the following is an appropriate boundary condition at the surface $S$ for solving the unsteady state, one-dimensional heat conduction equations for the hot plate and cold plate for $t>0$?
- In an adiabatic process, which of the following statements is true?
- JEE Main - 2025
- Physics
- Thermodynamics
The internal energy of air in $ 4 \, \text{m} \times 4 \, \text{m} \times 3 \, \text{m} $ sized room at 1 atmospheric pressure will be $ \times 10^6 \, \text{J} $. (Consider air as a diatomic molecule)
- JEE Main - 2025
- Physics
- Thermodynamics
- An ideal gas with an adiabatic exponent 1.5, initially at 27°C is compressed adiabatically from 800 cc to 200 cc. The final temperature of the gas is:
- JEE Main - 2025
- Chemistry
- Thermodynamics
- If \[ \text{C(diamond)} \rightarrow \text{C(graphite)} + X \, \text{kj mol}^{-1} \] \[ \text{C(diamond)} + \text{O}_2(g) \rightarrow \text{CO}(g) + Y \, \text{kj mol}^{-1} \] \[ \text{C(graphite)} + \text{O}_2(g) \rightarrow \text{CO}(g) + Z \, \text{kj mol}^{-1} \] At constant temperature. Then:
- JEE Main - 2025
- Chemistry
- Thermodynamics
Questions Asked in GATE CH exam
An electrical wire of 2 mm diameter and 5 m length is insulated with a plastic layer of thickness 2 mm and thermal conductivity \( k = 0.1 \) W/(m·K). It is exposed to ambient air at 30°C. For a current of 5 A, the potential drop across the wire is 2 V. The air-side heat transfer coefficient is 20 W/(m²·K). Neglecting the thermal resistance of the wire, the steady-state temperature at the wire-insulation interface __________°C (rounded off to 1 decimal place).
GIVEN:
Kinematic viscosity: \( \nu = 1.0 \times 10^{-6} \, {m}^2/{s} \)
Prandtl number: \( {Pr} = 7.01 \)
Velocity boundary layer thickness: \[ \delta_H = \frac{4.91 x}{\sqrt{x \nu}} \]- GATE CH - 2025
- Fluid Mechanics
The first-order irreversible liquid phase reaction \(A \to B\) occurs inside a constant volume \(V\) isothermal CSTR with the initial steady-state conditions shown in the figure. The gain, in kmol/m³·h, of the transfer function relating the reactor effluent \(A\) concentration \(c_A\) to the inlet flow rate \(F\) is:
- GATE CH - 2025
- Fluid Mechanics
- Consider a Cartesian coordinate system defined over a 3-dimensional vector space with orthogonal unit basis vectors \(\hat{i}, \hat{j}\), and \(\hat{k}\). Let vector \(\mathbf{a} = \sqrt{2}\hat{i} + \frac{1}{\sqrt{2}}\hat{k}\), and vector \(\mathbf{b} = \frac{1}{\sqrt{2}}\hat{i} + \sqrt{2}\hat{j} - \hat{k}\). The inner product of these vectors (\(\mathbf{a} \cdot \mathbf{b}\)) is:
- GATE CH - 2025
- Vector Algebra
- The sum of the following infinite series is: \[ 1 + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \dots \]
- GATE CH - 2025
- GATE BT - 2025
- GATE GG - 2025
- Sequence and Series
- A thin wire is used to construct all the edges of a cube of 1 m side by bending, cutting, and soldering the wire. If the wire is 12 m long, what is the minimum number of cuts required to construct the wire frame to form the cube?