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In this page we have *Important questions on heat and thermodynamics for JEE Main and Advanced* . Hope you like them and do not forget to like , social shar
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**Question 1:**
A composite slab is prepared by pasting three slab of thickness L

_{1},L

_{2},L

_{3} and thermal conductivity K

_{1},K

_{2},K

_{3}.The slab have equal cross-sectional area .Find the equivalent thermal conductivity

a.K

_{1}K

_{2}K

_{3}(L

_{1}+L

_{2}+L

_{3})/K

_{2}K

_{3}L

_{1}+K

_{1}K

_{3}L

_{2}+K

_{1}K

_{2}L

_{3}
b.K

_{2}K

_{3}L

_{1}+K

_{1}K

_{3}L

_{2}+K

_{1}K

_{2}L

_{3}/K

_{1}+K

_{2}+K

_{3}
c. K

_{1}+K

_{2}+K

_{3}/L

_{1}+L

_{2}+L

_{3}
d. L

_{1}+L

_{2}+L

_{3}/K

_{1}+K

_{2}+K

_{3}
Solution
R=R_{1}+R_{1}+R_{1}

L_{1}+L_{2}+L_{3}/KA=L_{1}/K_{1}A+L_{2}/K_{2}A+L_{3}/K_{3}A

K=K_{1}K_{2}K_{3}(L_{1}+L_{2}+L_{3})/K_{2}K_{3}L_{1}+K_{1}K_{3}L_{2}+K_{1}K_{2}L_{3}

**Question 2:**
Three black bodies are such that higher intensity wavelengths are in the ratio

λ

_{m1} : λ

_{m2} : λ

_{m3} = 1 :(21)

^{1/2}: (3)

^{1/2}
which of the these is true for the temperatures

a, T

_{1} > T

_{3} > T

_{2}
b, T

_{1} > T

_{2} > T

_{3}
c, T

_{3} > T

_{2} > T

_{1}
d, T

_{3} > T

_{1} > T

_{2}
Solution
. λ_{m1} = 1

λ_{m2} = (21)^{1/2}

λ_{m3}= (3)^{1/2}

so λ_{m2} λ_{m3} > λ_{m1}

so now as λ_{m}T= constant

so T_{1} > T_{3} > T_{2}

**Question 3:**
The tungsten element of the electric lamp has as surface area A and Power is P and emissivity is 0.4

a. Find the temperature of the filament

b. if the tungsten filament behave like blackbody ,find the % increase in power required to maintain the same temperature.

Solution
P=eσAT^{4}

T=(P/eσA)^{1/4}

If the body behaves like blackbody.

P^{'}=σAT^{4}

Substituting the value of T from last expression

P^{'}=P/e

% increase in Power

$%=\frac {(\frac {P}{e} -P)}{P} x 100=150%$

**Question 4:**
A Rod is initially at a uniform temperature at T

_{1}.One end is kept at T

_{1} and other end is kept in a furnace maintained at temperature at T

_{2}.(T

_{2} >T

_{1}).The Surface of the rod is insulated so that heat can flow lengthwise along the red-Light of the Rod is L, area A and thermal conductivity of the Rod is K. Consider a short cylindrical element of the rod of unit length .If the temperature gradient at the one end of the element is K

^{' }. Find the rate of flow across the element.

Solution
Q=KAK^{'}

**Question 5:**
A gas mixture consist of molecules of type A, B, C, D with molecular

masses M

_{a} > M

_{b} > M

_{c} >M

_{d}
Two statement are drawn from it

**A,** Average kinetic energy of four type of gases in the mixture are in the ratio

E

_{a}/1 =E

_{b}/1 =E

_{c}/1 =E

_{d}/1

**B,** Rms speed of molecules of the four types are in the order if V is the rms speed

V

_{D} > V

_{C} > V

_{C} > V

_{A}
which one of following is true

a, Only A correct

b, Only B correct

c, A & B both are correct

d, A & B both are wrong

Solution
Average kinetic energy is same for all the gases at the same temperature

rms speed is inversely proportional to the Molecular mass of the gas

since M_{a} > M_{b} > M_{c} >M_{d}

V_{D} > V_{C} > V_{C} > V_{A}

**Question 6:**
Calculate the variation of atmospheric pressure with elevation of the earth atmosphere. Considering the temperature to be uniform throughout(which is not the actual case)

Solution
From hydrostatic relation

dP/dY=-ρg---(1)

The density ρ is not constant but varies with the pressure. We know that ideal gas equation is

PV=nRT

or PV=mRT/M

and ρ=m/V

so ρ=PM/RT

putting this value in equation 1

dP/dY=-PMg/RT

Intregating on both side with upper and lower limit as (P_{2},P_{1}) on leftt side and (y_{2},y_{1}) on right side

∫dP/P=(-Mg/RT)∫dY

lnP_{2}/P_{1}=-Mg(y_{2}-y_{1})/RT

If at y=0,pressure is P_{0},then pressure p at an point y will be

P=P_{0}e^{-Mgy/RT}

Where M is the molecular mass of the air

**Question 7:**
An ideal gas sample of .203 gm occupies 1000cm

^{3} at STP. Calculate the RMS speed of the molecules

Solution
Mass of sample=.203 gm

V=1000cm^{3}

At STP

Pressure P=10^{5} pascal

Temperature T=0°C=273K

V_{rms}=√(3P/ρ)

Now ρ=m/V

So

V_{rms}=√(3PV/m)

Substituting all the values

V_{rms}=1215.6 m/s

**Question 8:**
How will the rate of collision of a rigid diatomic molecules against the vessel will change ,if the gas is expanded adiabatically η times

Solution
Rate of collision of molecules against the vessel wall is given by

$c= \frac {1}{6} (\frac {N}{V}) v_rms$

Where N is the no of molecules in Volume V

According to kinetic theory v_{rms} is given by

$v_rms =\sqrt { \frac {3RT}{M}}$

So we can say that

$c \alpha \sqrt {\frac {T}{V^2}}$

Let take c_{1 } be the initial rate of collision and c_{2} be the final rate of collision after the expansion

Then we can say

$\frac {c_1}{c_2} = \sqrt {\frac {T_1 V_2^2}{T_2 V_1^2}}$ ---(1)

Now we know that for adiabatic process

$\frac {T_2}{T_1}= (\frac {V_1}{V_2})^ {\gamma -1}$

Or

$\frac {T_1}{T_2}= (\frac {V_2}{V_1})^ {\gamma -1}=\eta ^ {\gamma -1}$ --(2)

As V_{2}/V_{1}=η

From equation (1) and (2)

$\frac {c_1}{c_2}=\sqrt {\eta ^ {\gamma -1}}$

**Question 9:**
Which one of the following statement is true about a gas undergoing isothermal change

a) The temperature of the gas is constant

b) The pressure of the gas remains constant

c) the volume of the gas remains constant

d) The gas is completely insulated from the surrounding’s

Solution
Correct ans is a

**Question 10:**
Which of the following devices is used to detect thermal radiation?

a)Thermopile

b) Constant volume air thermometer

c) Liquid thermometer

d) Six Maximum and minimum thermometer

Solution
Answer is a

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