A box Of interior Volume $V_1$ has a heavy airtight hinged lid of mass M and area A.The box contains n

find the pressure of the gas in the box

a. n

b. n

c. (n

d. none of the above.

Applying Ideal gas equation

P_{1} V_{1}=n_{1}RT_{0}

or P_{1}=n_{1}RT_{0}/V_{1}

find the pressure of the gas in the chamber

a. n

b. n

c. (n

d. none of the above.

Applying Ideal Gas equation

P_{2} V_{2}=n_{2}RT_{0}

or P_{2}=n_{2}RT_{0}/V_{2}

Initially the hinged lid is closed.Then which of these expression is true

a.n

b. n

c. n

d. n

The lid would lift if the net upward pressure force (P_{1}-P_{2})A exceeded the weight Mg

The fact that the lid is closed therefore implies that (P_{1}-P_{2})A <=Mg

If the whole system is heated,at what temperature T will the gas pressure lift the hinged lid

a. T=(Mg/RA)(n

b. T=(Mg/RA)(n

c. T=(Mg/RA)(n

d. None of the above

it will lift when (P_{1}-P_{2})A =Mg

n_{1}RT/V_{1}-n_{2}RT/V_{1}=Mg/A

or T=(Mg/RA)(n_{1}/V_{1} -n_{2}/V_{2})

or n_{1}RT_{0}/V_{1} -n_{2}RT_{0}/V_{2} <=Mg/A

In the vander waals equation

(P+a/V

a. a and b are the correction for the cohesive forces

b. a and b are the correction for the volume occupied by the molecules.

c. a is the correction for the volume occupied by the molecules and b is the correction for the cohesive forces

d. a is the correction for the cohesive forces and b is the correction for the volume occupied by the molecules

(d)

An gas obeys Vander waals equation

(P+a/V

The dimensional formula for constant a is

a. ML

b. ML

c. ML

d. M

(a)
For dimensional consistency,the dimension of a/V^{2} must be same as those of P.therefore ,the dimensions of a are same as those of that

PV^{2}=ML^{-1}T^{-2}X (L^{3})^{2}=ML^{5}T^{-2}

Find the work done by this gas when gas expand from V to 2V at constant temperature T

a.nRTlog

b.nRTlog

c. nRTlog

d. none of the above

(b)
Given (P+a/V^{2})(V-b)=nRT

or P+a/V^{2}=nRT/(V-b)

or P=[nRT/(V-b)]-[a/V^{2}]

Work done=∫PdV

Integrating with limits (V,2V)

=nRT[∫(dV/V-b)] -a[∫(dV/V^{2}]

=nRTlog_{e}[(2V-b)/(V-b)] +a/V

Assertion and Reason

a. Statement I is true ,statement II is true ,statement II is correct explanation for statement I

b. Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I

c. Statement I is true,Statement II is false

d. Statement I is False,Statement II is True

a. Statement I is true ,statement II is true ,statement II is correct explanation for statement I

b. Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I

c. Statement I is true,Statement II is false

d. Statement I is False,Statement II is True

STATEMENT 1:Real Gases behave like ideal gas at high temperature

STATEMENT 2:Intermolecular forces are negligible at high temperature

(a)

STATEMENT 1:Equation of state for a real gas is (P+a/V2)(V-b)=nRT

STATEMENT 2: Molecular attraction is not negligible and the size of molecules are not negligible in comparison to average separation between them

(a)

STATEMENT 1:The pressure exerted by a gas is the same irrespective of the size of the molecules

STATEMENT II:Molecular collisions will invariably change the velocities of individual molecules but the number of the molecules having any particular velocity will remain change

Solution