# Ideal Gas Laws Problems

A box Of interior Volume $V_1$ has a heavy airtight hinged lid of mass M and area A.The box contains n1 moles of gas at Temperature T0.The box is inside a chamber which also contains additional n2 moles of the same gas at the same temperature..The gas in the chamber occupies the volume V2.

Question 1
find the pressure of the gas in the box
a. n1RT0/V1
b. n2RT0/V2
c. (n1+n2)RT/V1+V2
d. none of the above.

Applying Ideal gas equation
P1 V1=n1RT0
or P1=n1RT0/V1

Question 2
find the pressure of the gas in the chamber
a. n1RT0/V1
b. n2RT0/V2
c. (n1+n2)RT/V1+V2
d. none of the above.

Applying Ideal Gas equation
P2 V2=n2RT0
or P2=n2RT0/V2

Question 3
Initially the hinged lid is closed.Then which of these expression is true
a.n1RT0/V1 -n2RT0/V2 <=Mg/A
b. n1RT0/V1 -n2RT0/V2 => Mg/A
c. n2RT0/V2 -n1RT0/V1 => Mg/A
d. n2RT0/V2 -n1RT0/V1 <= Mg/A

The lid would lift if the net upward pressure force (P1-P2)A exceeded the weight Mg
The fact that the lid is closed therefore implies that (P1-P2)A <=Mg

Question 4
If the whole system is heated,at what temperature T will the gas pressure lift the hinged lid
a. T=(Mg/RA)(n1/V1 -n2/V2)
b. T=(Mg/RA)(n2/V2 -n1/V1)
c. T=(Mg/RA)(n1/V1 +n2/V2)
d. None of the above

it will lift when (P1-P2)A =Mg
n1RT/V1-n2RT/V1=Mg/A
or T=(Mg/RA)(n1/V1 -n2/V2)
or n1RT0/V1 -n2RT0/V2 <=Mg/A

## Multiple choice questions with one or more answer

Question 5
In the vander waals equation
(P+a/V2)(V-b)=nRT

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/V2)(V-b)=nRT

Question 6
The dimensional formula for constant a is
a. ML5T-2
b. ML5T-1
c. ML-1T-1
d. M0L-0T0

(a) For dimensional consistency,the dimension of a/V2 must be same as those of P.therefore ,the dimensions of a are same as those of that
PV2=ML-1T-2X (L3)2=ML5T-2

Question 7
Find the work done by this gas when gas expand from V to 2V at constant temperature T
a.nRTloge(2V-b/V-b) -a/V
b.nRTloge(2V-b/V-b) +a/V
c. nRTloge(2V-b/V-b)
d. none of the above

(b) Given (P+a/V2)(V-b)=nRT
or P+a/V2=nRT/(V-b)
or P=[nRT/(V-b)]-[a/V2]

Work done=∫PdV
Integrating with limits (V,2V)
=nRT[∫(dV/V-b)] -a[∫(dV/V2]
=nRTloge[(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
Question 8
STATEMENT 1:Real Gases behave like ideal gas at high temperature
STATEMENT 2:Intermolecular forces are negligible at high temperature

(a)

Question 9
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