Match the LIST-I with LIST-II Choose the correct answer from the options given below: 
To solve this problem, we need to match the type of gas (List-I) with the specific heat capacity ratio \( \frac{C_p}{C_v} \) (List-II). Here's a step-by-step explanation:
1. **Understanding the Specific Heat Capacity Ratio \(\frac{C_p}{C_v}\):**
- The ratio \(\gamma = \frac{C_p}{C_v}\) is defined as the specific heat ratio of gases.
- For a monoatomic gas, \(\gamma\) is usually around \(\frac{5}{3}\).
- For a diatomic non-rigid gas, \(\gamma\) is typically \(\frac{7}{5}\).
- For a diatomic rigid gas, \(\gamma\) is usually near \(\frac{9}{7}\).
- For a triatomic rigid gas, \(\gamma\) might be \(\frac{4}{3}\).
2. **Matching the Lists:**
- **A. Triatomic rigid gas:** \(\frac{C_p}{C_v} = \frac{4}{3}\) (III)
- **B. Diatomic non-rigid gas:** \(\frac{C_p}{C_v} = \frac{7}{5}\) (IV)
- **C. Monoatomic gas:** \(\frac{C_p}{C_v} = \frac{5}{3}\) (I)
- **D. Diatomic rigid gas:** \(\frac{C_p}{C_v} = \frac{9}{7}\) (II)
Therefore, the correct match is:
- A-III: Triatomic rigid gas is matched with \(\frac{C_p}{C_v} = \frac{4}{3}\).
- B-IV: Diatomic non-rigid gas is matched with \(\frac{C_p}{C_v} = \frac{7}{5}\).
- C-I: Monoatomic gas is matched with \(\frac{C_p}{C_v} = \frac{5}{3}\).
- D-II: Diatomic rigid gas is matched with \(\frac{C_p}{C_v} = \frac{9}{7}\).
Thus, the correct answer is A-III, B-IV, C-I, D-II.
Similar Questions
During the melting of a slab of ice at $273 \ K$ at atmospheric pressure:
- $\gamma_A$ is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. $\gamma_B$ is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If $\frac{\gamma_A}{\gamma_B} = \left(1 + \frac{1}{n}\right)$, then the value of n is _________.
- Match List - I with List - II.$\Delta Q$=Heat supplied
List - I List - II (A) Isobaric (I) $\Delta Q = \Delta W$ (B) Isochoric (II) $\Delta Q = \Delta U$ (C) Adiabatic (III) $\Delta Q = \text{zero}$ (D) Isothermal (IV) $\Delta Q = \Delta U + P\Delta V$
$\Delta W$ = Work done by the system
$\Delta U$=Change in internal energy
P = Pressure of the system
$\Delta V$ = Change in volume of the system
Choose the correct answer from the options given below : - There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K, at steady state the pressure in the vessels will be (in kPa).
An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ________ $\times 10^{-1}$J.
(Take $\pi = 3.14$)
- An ideal gas exists in a state with pressure $P_0$, volume $V_0$. It is isothermally expanded to $4$ times of its initial volume($V_0$), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is
Water falls from a height of $200 \text{ m}$ into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool.
(Take $g = 10 \text{ m/s}^2$, specific heat of water $= 4200 \text{ J/(kg K)}$)
A monoatomic gas having $\gamma = \frac{5}{3}$ is stored in a thermally insulated container and the gas is suddenly compressed to $\frac{1}{8}^{\text{th}}$ of its initial volume. The ratio of final pressure and initial pressure is:
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- A body takes 10 minutes to cool from $60^\circ C$ to $50^\circ C$. The temperature of surroundings is constant at $25^\circ C$. Then, the temperature of the body after next 10 minutes will be approximately :
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Important Questions from Heat and Thermodynamics
During the melting of a slab of ice at $273 \ K$ at atmospheric pressure:
- $\gamma_A$ is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. $\gamma_B$ is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If $\frac{\gamma_A}{\gamma_B} = \left(1 + \frac{1}{n}\right)$, then the value of n is _________.
- Match List - I with List - II.$\Delta Q$=Heat supplied
List - I List - II (A) Isobaric (I) $\Delta Q = \Delta W$ (B) Isochoric (II) $\Delta Q = \Delta U$ (C) Adiabatic (III) $\Delta Q = \text{zero}$ (D) Isothermal (IV) $\Delta Q = \Delta U + P\Delta V$
$\Delta W$ = Work done by the system
$\Delta U$=Change in internal energy
P = Pressure of the system
$\Delta V$ = Change in volume of the system
Choose the correct answer from the options given below : - There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K, at steady state the pressure in the vessels will be (in kPa).
An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ________ $\times 10^{-1}$J.
(Take $\pi = 3.14$)
