Question:
For an ideal gas, internal energy is a function of:
For an ideal gas, internal energy is a function of:
Show Hint
For real gases, internal energy is a function of both temperature and volume \( U = f(T, V) \) due to intermolecular forces.
However, for ideal gases, Joule's law holds perfectly.
However, for ideal gases, Joule's law holds perfectly.
Updated On: Feb 9, 2026
- Pressure only
- Volume only
- Temperature only
- Pressure and volume
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to inter-particle interactions.
The internal energy \( (U) \) of a substance is the sum of the kinetic and potential energies of its molecules.
Step 2: Key Formula or Approach:
According to Joule's Law for an ideal gas:
\[ U = f(T) \]
The change in internal energy is given by:
\[ dU = m C_v dT \]
Where \( C_v \) is the specific heat at constant volume and \( T \) is the absolute temperature.
Step 3: Detailed Explanation:
In an ideal gas, there are no intermolecular forces of attraction or repulsion (potential energy is zero).
Thus, the internal energy consists solely of kinetic energy.
According to the kinetic theory of gases, the average kinetic energy of gas molecules is directly proportional to the absolute temperature.
Therefore, the internal energy of an ideal gas does not depend on pressure or volume, but only on temperature.
Step 4: Final Answer:
Internal energy is a function of temperature only for an ideal gas.
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to inter-particle interactions.
The internal energy \( (U) \) of a substance is the sum of the kinetic and potential energies of its molecules.
Step 2: Key Formula or Approach:
According to Joule's Law for an ideal gas:
\[ U = f(T) \]
The change in internal energy is given by:
\[ dU = m C_v dT \]
Where \( C_v \) is the specific heat at constant volume and \( T \) is the absolute temperature.
Step 3: Detailed Explanation:
In an ideal gas, there are no intermolecular forces of attraction or repulsion (potential energy is zero).
Thus, the internal energy consists solely of kinetic energy.
According to the kinetic theory of gases, the average kinetic energy of gas molecules is directly proportional to the absolute temperature.
Therefore, the internal energy of an ideal gas does not depend on pressure or volume, but only on temperature.
Step 4: Final Answer:
Internal energy is a function of temperature only for an ideal gas.
Was this answer helpful?
0
0
Top GATE CH Process Calculations and Thermodynamics Questions
- Consider a vapour-liquid mixture of components A and B that obeys Raoult's law. The vapour pressure of A is half that of B. The vapour phase concentrations of A and B are 3 mol m\(^{-3}\) and 6 mol m\(^{-3}\), respectively. At equilibrium, the ratio of the liquid phase concentration of A to that of B is:
- Consider a binary mixture of components A and B at temperature \( T \) and pressure \( P \). Let \( \vec{V}_A \) and \( \vec{V}_B \) be the partial molar volumes of A and B, respectively. At a certain mole fraction of A, \( X_A \):
\[ \left( \frac{\partial \vec{V}_A}{\partial X_A} \right)_{T,P} = 22 \text{ cm}^3 \text{ mol}^{-1} \quad \text{and} \quad \left( \frac{\partial \vec{V}_B}{\partial X_A} \right)_{T,P} = -18 \text{ cm}^3 \text{ mol}^{-1} \]
The value of \( X_A \), rounded off to 2 decimal places, is ____. - The Newton-Raphson method is used to solve \( f(x) = 0 \), where \( f(x) = e^x - 5x \). Starting with an initial guess \( x^{(0)} = 1.0 \), the value of the next iterate \( x^{(1)} \), rounded off to 2 decimal places, is _____
- An isolated system consists of two perfectly sealed cuboidal compartments A and B separated by a movable rigid wall of cross-sectional area 0.1 m\(^2\) as shown in the figure. Initially, the movable wall is held in place by latches L1 and L2 such that the volume of compartment A is 0.1 m\(^3\). Compartment A contains a monoatomic ideal gas at 5 bar and 400 K. Compartment B is perfectly evacuated and contains a massless Hookean spring of force constant 0.3 N m\(^{-1}\) at its equilibrium length (stored elastic energy is zero). The latches L1 and L2 are released, the wall moves to the right by 0.2 m, where it is held at the new position by latches L3 and L4. Assume all the walls and latches are massless. The final equilibrium temperature of the gas in compartment A, in K, rounded off to 1 decimal place, is ______.
- Ethylene obeys the truncated virial equation-of-state \( \frac{PV}{RT} = 1 + \frac{BP}{RT} \) where \( P \) is the pressure, \( V \) is the molar volume, \( T \) is the absolute temperature, and \( B \) is the second virial coefficient. The universal gas constant \( R = 83.14 \) bar cm\(^3\) mol\(^{-1}\) K\(^{-1}\). At 340 K, the slope of the compressibility factor (\( Z \)) vs. pressure curve is \( -3.538 \times 10^{-3} \) bar\(^{-1}\). Let \( G_R \) denote the molar residual Gibbs free energy. At these conditions, the value of \( \left( \frac{\partial G_R}{\partial P} \right)_T \), in cm\(^3\) mol\(^{-1}\), rounded off to 1 decimal place, is _____.
View More Questions
Top GATE CH Thermodynamics Questions
- The number of independent intensive variables that need to be specified to determine the thermodynamic state of a ternary mixture at vapor-liquid-liquid equilibrium is:
- The boundary of a system does not allow exchange of either mass or energy (in the form of heat and/or work) with the surroundings. The system is termed
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).Ideal nonreacting gases A and B are contained inside a perfectly insulated chamber, separated by a thin partition, as shown in the figure. The partition is removed, and the two gases mix till final equilibrium is reached. The change in total entropy for the process is \( \_\_ \) J/K (rounded off to 1 decimal place).
Given: Universal gas constant \( R = 8.314 \) J/(mol K), \( T_A = T_B = 273 \) K, \( P_A = P_B = 1 \) atm, \( V_B = 22.4 \) L, \( V_A = 3V_B \).
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 $t>0$?
View More Questions
Top GATE CH Questions
- Consider a Leniar Homogeneous system AX = 0, where A is N × N matrix and X is N × 1 vector. When we solve this 0 is null matrix of N × 1. Let R be the rank matrix for a for a Non-trivial solution.
- Which are true for Petroleum / Petrochemicals?
- F(x) = ex - 5x and the value of X0 = 1 then what will be the value of X1?
- The first non-zero term in the taylor series expansion of (1 - x) - e- x, about x = 0
- \(\frac{P}{Q}\) is not equal 1, \(\left(\frac{P}{Q}\right)^{\frac{P}{Q}} = P^{\frac{P}{Q} - 1}\)
View More Questions