A mixture of one mole of a monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature (\(27^\circ \text{C}\)). The ratio of specific heat of gases at constant volume respectively is:
- \(\frac{7}{5}\)
- \(\frac{3}{2}\)
- \(\frac{3}{5}\)
- \(\frac{5}{3}\)
The Correct Option is C
Solution and Explanation
The specific heat capacities at constant volume are:
\[ (C_V)_{\text{mono}} = \frac{3}{2}R, \quad (C_V)_{\text{dia}} = \frac{5}{2}R. \]
The ratio is:
\[ \frac{(C_V)_{\text{mono}}}{(C_V)_{\text{dia}}} = \frac{\frac{3}{2}R}{\frac{5}{2}R} = \frac{3}{5}. \]
Final Answer: \(3 : 5\).
Top Questions on Thermodynamics
- 500 J of energy is transferred as heat to 0.5 mol of Argon gas at 298 K and 1.00 atm. The final temperature and the change in internal energy respectively are: Given \( R = 8.3 \, \text{J K}^{-1} \text{mol}^{-1} \).
- JEE Main - 2025
- Chemistry
- Thermodynamics
- Given below is the plot of the molar conductivity vs \( \sqrt{c} \) concentration for KCl in aqueous solution. If, for the higher concentration of KCl solution, the resistance of the conductivity cell is 100 \( \Omega \), then the resistance of the same cell with the dilute solution is 'x' \( \Omega \). The value of \( x \) is:
- JEE Main - 2025
- Chemistry
- Thermodynamics
For a given reaction \( R \rightarrow P \), \( t_{1/2} \) is related to \([A_0]\) as given in the table. Given: \( \log 2 = 0.30 \). Which of the following is true?
\([A]\) (mol/L) \(t_{1/2}\) (min) 0.100 200 0.025 100 A. The order of the reaction is \( \frac{1}{2} \).
B. If \( [A_0] \) is 1 M, then \( t_{1/2} \) is \( 200/\sqrt{10} \) min.
C. The order of the reaction changes to 1 if the concentration of reactant changes from 0.100 M to 0.500 M.
D. \( t_{1/2} \) is 800 min for \( [A_0] = 1.6 \) M.- JEE Main - 2025
- Chemistry
- Thermodynamics
- Ice and water are placed in a closed container at a pressure of 1 atm and temperature 273.15K. If pressure of the system is increased 2 times, keeping temperature constant, then identify correct observation from the following:
- JEE Main - 2025
- Chemistry
- Thermodynamics
- What is the freezing point depression constant of a solvent, 50 g of which contain 1 g non-volatile solute (molar mass 256 g mol\(^{-1}\)) and the decrease in freezing point is 0.40 K?
- JEE Main - 2025
- Chemistry
- Thermodynamics
Questions Asked in JEE Main exam
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to:
- JEE Main - 2025
- Arithmetic and Geometric Progressions
- Let ABCD be a trapezium whose vertices lie on the parabola \( y^2 = 4x \). Let the sides AD and BC of the trapezium be parallel to the y-axis. If the diagonal AC is of length \( \frac{25}{4} \) and it passes through the point \( (1, 0) \), then the area of ABCD is:
- JEE Main - 2025
- Coordinate Geometry
- If \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{96x^2 \cos^2 x}{1 + e^x} dx = \pi(a\pi^2 + \beta), \quad a, \beta \in \mathbb{Z}, \] then \( (a + \beta)^2 \) equals:
- JEE Main - 2025
- Integration
- The maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer at rest on the river bank is cm. (Take g = 10 m/s²).
- JEE Main - 2025
- projectile motion
- Let \( \vec{a} = \hat{i} + 2\hat{j} + \hat{k} \) and \( \vec{b} = 2\hat{i} + 7\hat{j} + 3\hat{k} \). Let \( L_1 : \vec{r} = (-\hat{i} + 2\hat{j} + \hat{k}) + \lambda \vec{a}, \lambda \in {R} \) and \( L_2 : \vec{r} = (\hat{j} + \hat{k}) + \mu \vec{b}, \mu \in \mathbb{R} \) be two lines. If the line \( L_3 \) passes through the point of intersection of \( L_1 \) and \( L_2 \), and is parallel to \( \vec{a} + \vec{b} \), then \( L_3 \) passes through the point:
- JEE Main - 2025
- Vectors