Exams › JEE Advanced › Physics

A sealed vessel of volume V initially contains gas at pressure P0. Gas is evacuated isothermally at a constant volumetric rate C (volume measured at instantaneous pressure). Which of the following options are correct?

1. Pressure P at time t is P0 * e^(-C*t/V)
2. Pressure P at time t is P0 - C*t/V
3. Number of moles evacuated in time t is linearly proportional to t
4. Number of moles evacuated in time t is exponentially dependent on t

Correct answer: Pressure P at time t is P0 * e^(-C*t/V)

Solution

Since the vessel volume V is fixed and process is isothermal, n proportional to P. Rate of moles removed = C*P/(RT) (rate of volume removed * density at current pressure). moles in vessel n = PV/(RT). dn/dt = V/(RT) * dP/dt = -C*P/(RT). So dP/dt = -CP/V. Solution: P = P0*e^(-Ct/V). Moles evacuated = integral of C*P/(RT) dt = C*P0/(RT) * integral e^(-Ct/V) dt = (P0*V/RT)*(1 - e^(-Ct/V)). This is exponential in t, not linear. So options 1 and 4 are correct.

Related JEE Advanced Physics questions

• Consider an ideal diatomic gas with molecules of mass 'm' at an absolute temperature T. Let V represent the root mean square speed of the molecules, ignoring vibrational energy contributions. Which statement is incorrect?
• The average kinetic energy of a single atom is calculated as (3/2)kT, where k = 1.38 × 10⁻²³ J/K and T = 160 K. What is the resulting value?
• Two non-reactive monatomic ideal gases have their atomic masses in the ratio 2:3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4:3. The ratio of their densities is
• A gas is enclosed in a container at pressure P and absolute temperature T. If k is the Boltzmann constant, the number of gas molecules per unit volume is:
• An ideal gas is in thermodynamic equilibrium at fixed temperature and pressure. A molecule of the gas has n degrees of freedom. Let Uₙ denote the molar internal energy and vₙ denote the speed of sound in the gas when the degrees of freedom are n. Which of the following statements is correct?
• In a mixture of argon and nitrogen gases at room temperature, consider a single collision between one argon molecule and one nitrogen molecule. Which of the following outcomes are physically possible?

⚔️ Practice JEE Advanced Physics free + battle 1v1 →