Assertion (A): The pressure exerted by an enclosed ideal gas does not depend on the shape of the container.
Reason (R): The pressure of an ideal gas depends on the number of moles, temperature and volume of the enclosure.
Pressure of an ideal gas is given by \( PV = nRT \). For a fixed amount of gas at a given temperature, P depends on V, not shape. So, (A) is true. Also, \( P = \frac{nRT}{V} \), so P depends on n, T, V. So, (R) is true. (R) correctly explains that since the ideal gas law depends only on V (not shape for a given V), A is true.
Assertion (A): The ratio \( \frac{C_P}{C_V} \) is more for helium gas than for hydrogen gas.
Reason (R): Atomic mass of helium is more than that of hydrogen.
For Helium (monoatomic), \( \gamma = 5/3 \). For Hydrogen (diatomic), \( \gamma = 7/5 \). Since \( 5/3 > 7/5 \), (A) is true. Atomic mass of He is 4 amu, H is 1 amu (H2 is 2 amu), so (R) is true.
However, \( \gamma \) depends on degrees of freedom (monoatomic vs diatomic), not atomic mass. So, (R) is not the correct explanation.
Assertion (A): On a V-T graph, the slope of an isobar increases with pressure.
Reason (R): At constant temperature, for an ideal gas its volume is directly proportional to its pressure.
For an isobar, \( V = (\frac{nR}{P})T \). The slope on a V-T graph is \( \frac{nR}{P} \). As P increases, slope decreases, so (A) is false. Boyle's law states that at constant T, \( V \propto \frac{1}{P} \), i.e., V is inversely proportional to P, so (R) is false.
Assertion (A): Internal energy of real gas is always negative at absolute zero temperature.
Reason (R): Potential energy of a bounded system is negative.
At absolute zero, kinetic energy is minimal (zero for ideal gas). For a real gas, attractive intermolecular forces mean potential energy is negative (relative to infinite separation). So, total internal energy is negative. Thus, (A) is true. (R) is also true, as attractive forces in a bounded system lead to negative potential energy. (R) explains (A).
Assertion (A): For an ideal gas, at constant temperature, the product of the pressure and volume is constant.
Reason (R): The mean square velocity of gas molecules is inversely proportional to mass of molecule.
Boyle's Law states that for an ideal gas at constant T, \( PV = \text{constant} \). So (A) is true. The mean square velocity \( = \frac{3kT}{m} \), so it is inversely proportional to molecular mass m.
So (R) is true. However, (R) does not explain Boyle's law (A).
For \(n\) mole of an ideal gas, the correct equation of \(1^{\text{st}}\) law of thermodynamics corresponding to isobaric process will be (symbols have their usual meanings)
According to the first law of thermodynamics, \(Q = \Delta U + W\). For an isobaric process, the work done is \(W = P\Delta V = nR\Delta T\). Therefore, both equations (1) and (2) are correct representation.
Heat and work depend on the path taken by the system during a thermodynamic process, making them path functions. Internal energy is a state function as it depends only on the initial and final states of the system.
In ideal condition, the maximum efficiency that can be derived from a heat engine built operating between \(600\text{ K}\) reservoir and \(200\text{ K}\) sink, is
The maximum efficiency is given by the Carnot efficiency formula: \(\eta = 1 - \frac{T_2}{T_1}\). Here, \(T_1 = 600\text{ K}\) and \(T_2 = 200\text{ K}\), so \(\eta = 1 -\frac{200}{600} = 1 - \frac{1}{3} = \frac{2}{3} \approx 66.67%\).
Which of the following is not the correct assumption of kinetic theory of gases?
One of the postulates of the kinetic theory of gases is that gas molecules collide elastically with each other as well as with the walls of the container. Hence, the assumption that there are no collisions among molecules is incorrect.