OBJECTIVE- HEAT THERMO 1:
Calculate the root mean square speed of smoke particles of mass −17 kg in in Brow Browni nian an mot motio ion n in air air at at NTP NTP. Boltz Boltzma mann nn 5 × 10 constant k=
1.38 × 10
−23
JK
−1
(!
1." cm#s
(B!
$.$ cm#s
(C!
$.% cm#s
(&!
'.' cm#s
Ans. (a) (a) $:
&uring an eperiment an ideal gas is found to o)e* an additional additional 2 initiall* at temp temp T and ,olume ,olume -. hat law VP + constant. The gas is initiall* will )e the temperature of the gas when it epands to a ,olume $-/ (! (B! T ʹ = 4 T Tʹ = 2 T (C!
T
ʹ=
5
T
(&!
T
ʹ=
6
T
Ans. (b) (b) 0.%" e ha,e two ,essels of equal ,olume2 one filled with h*drogen and o the other with with equal mass of 3elium. The common common temperature temperature is $4 C. %:
hat is the relati,e num)er of molecules in the two ,essels / (B! nH nH 1 5 (! = =
nHe nH (C!
nHe
=
1 2
nHe nH
(&!
1
nHe
=
1 3 1
Ans. (C) (C) ':
5f pressure of 3*drogen is $ atm2 what is the pressure of 3elium / (!
He ! 2 a"#.
(B!
He ! 3 a"#.
(C!
He ! $ a"#.
(&!
He ! 1 a"#.
Ans. (%) (%) ":
o
5f the temperature of 3elium is kept at $4 C and that of h*drogen is changed2 at what temperature will its pressure )ecome equal to that of helium / The molecular weights of h*drogen and helium are $ and ' respecti,el*. respecti,el*.
Ans. (a) (a)
o
(B!
−1'6 C
o
(&!
−18% C
(!
−1$% C
(C!
−176 C
Ans. (a)
o o
0.416.The pressure of a monoatomic gas increases linearl* from $ $ % 5 5 $ × 10 N#m 8 × 10 N#m when its ,olume increases from 6.$ m to to % 6." m . Calculate 4:
work done )* the gas "
(B!
1.8916
"
(&!
1.8916
(!
$.8916
(C!
1.8916
7
$
Ans. (C) 8:
increase in internal energ* (! (C!
Δ&
= $.8 × 10
5
4
(B!
J
ΔU = 4.8×10 J 6
ΔU = 6.8 ×10
5
(&!
ΔU = 4.8×10 J
J
Ans. (a) ;:
amount of heat supplied 5 8.6 ×10 (! J
(C!
5
(B!
12.6 ×10 J 5
5
6.6.×10 J
(&!
10.6 ×10 J
Ans. (C) 16:
molar heat capacit* of the gas <= + 8.%1 #mol k> (!
20.1 J'#K
(B!
1*.1$ J'#K
(C!
18.1$ J'#K
(&!
20.1$ J'#K
Ans. (b) o
0.111%.Two moles of 3elium gas ( γ + "#%! are initiall* at temperature $4 C and occup* a ,olume of $6 litres. The gas is first epanded at constant pressure until the ,olume is dou)led. Then it undergoes an adia)atic change until the temperature returns to its initial ,alue. 11:
hat are the final ,olume. (!
113.13×10
(C!
313.13×10
−3
3
m
−3
3
m
Ans. (A) 1$:
hat are the final pressure of gas/ 5
2
5
2
(!
0.44×10 N / m
(C!
0.94×10 N / m
1%:
hat is the work done )* the gas/ (?as constant = + 8.% T#mole @! (B! 13450 14450 J (! J (&! 12450 J (C! 16450
J
Ans. (%) 1'1". hen 1 gm of water changes from liquid to ,apour phase at % constant pressure of 1 atmosphere2 the ,olume increases from 1 cm to 1741 c.c. The heat of ,aporization at this pressure is "'6 cal#gm. Aind 1':
The work done (in ! in change of phase 170.78 J+e (! (B! (C!
1,0. *8 J+e
200.67 J+e
(&!
18.* J+e
Ans. (%) 1":
5ncrease in internal energ* of water. (!
20,,.33 J
(B!
30,,.33 J
(C!
$0,,.33 J
(&!
50,,.33 J
Ans. (a) 17: glass flask of ,olume one litre at 0 C is filled le,el full of mercur* at this o temperature. The flask and mercur* are now heated to 166 C. 3ow much mercur* will spill out if coefficient of ,olume epansion of mercur* is −$ −$ ' C and linear epansion of glass is 0.1× 10 ' C 1.82 × 10 respecti,el*/ (!
1$.2 ..
(B!
15.2
.. (C!
18.2 ..
(&!
20.2 ..J
Ans. (b) T n%es A an% B 4""e% " s"ns n"an e6+a a#+n"s 4 an 14 / %ea %a"# 7as a" 300K. Te s"n A s 4ee " #e9 e "a" 4 B s e% 4:e%. Te sa#e a#+n" 4 ea" s 7en " "e 7as n ea n%e. I4 "e se n "e#ea"+e 4 "e 7as n A s 30K9 "en "e se n "e#ea"+e 4 "e 7as n B s. (! (C! 18:
%6@
"6@
86 gm of water at 30 C is poured on a large )lock of ice at 0 C . The mass of ice that melts is (!
%6 gm
1;:
gas at pressure P is contained in a ,essel. 5f the masses of all the molecules are hal,ed pressure would )e (!
and
their
speeds
'P o
(B!
dou)led2
the
resulting
$P o P
(C! $6:
P o
(&!
2
The ,olume - ,ersus temperature T graphs for a certain amount of a perfect gas at two pressures P 1 and P $ are shown in the figure. 3ere (!
P1 P $
(B!
P1 P $
; a e4e" 7as9 PV =
Dolution:
#
P2 V
P1
RT
M ⇒
=
#R RT PM
<9 "e se 4 "e 7a s
#R PM
<e
∝
1 P
Hene P1 = P2 Hene9 (C) s e"
$1:
t room temperature the rms speed of the molecules of a certain diatomic gas is found to )e 1;%6 m#s. The gas is F 2 (B! (! H 2 Cl 2 (&! (C! O 2
Dolution: 3RT 3:8.31:30 0 −3 = M= = 2.00*8 :10 k7 2 2 V#s (1,30 )
I" s #e+a e7" 4 %7en
.
$$:
The latent heat of ,aporization of water is $$'6 . 5f the work done in the process of ,aporization of 1 gm is 178 2 then increase in internal energ* is (!
$'68
(B!
$$'6
(C!
$64$
(&!
1;6'
Hene9 (C) s e" $%:
; a 7as9 ! 1.28. >a" s "e n+#be 4 %e7ees 4 4ee%# 4 "e #e+as 4 "s 7as ? (!
%
(B!
"
(C!
7
(&!
4
ns. (d! $':
hich of the following temperatures is the highest/ (!
166 @ o
(C! Dolution: $" /
E$6 C o
o
(B!
E1% A
(&!
E%6 C
o
o
(B ! E1% A is (1%F%$! )elow ice point on A scale.
An %ea 7as ( γ ! 1.5) s e:an%e% a%aba"a. H #an "#es as "e 7as " be e:an%e% " e%+e "e " #ean s6+ae e" 4 #e+es 2.0 "#es (!
' times
(B!
17 times
(C!
8 times
(&!
$ times
ns. (B!
Hene9 (B) s e" $7:
thin copper wire of length G increases in length )* 1H when heated from 0 C to 100 C . 5f a thin copper plate of area 2@ × is heated from @
0 C to
100
C 2 the percentage increase in its area will
)e (! 1H
(B!
$H
(C!
(&!
'H
%H
ns. ()!
$4:
?as at pressure P o is contained in a ,essel. 5f the masses of all the molecules are dou)led pressure P will )e equal to (!
$P o
(C!
P o
ns. (d! $8: The molar heat capacit* in a process of a diatomic gas if it does a of 0#'2 when 0 amount of heat is supplied to it is 2
(!
5
R
10
(C!
3
R
5
(B! (&!
2
*
work
R
R
ns. (C! $;:
Aor an ideal gas: (!
the change in internal energ* in a constant pressure process from temperature T 1 to T $ is equal to nC , (T $ T 1 !2 where C , is the molar specific heat at constant ,olume and n the num)er of moles of the gas. (B!
the change in internal energ* of the gas and the work done )* the gas are equal in magnitude in an adia)atic process.
(C!
the internal energ* does not change in an isothermal process.
(&!
no heat is added or remo,ed in an adia)atic process.
(!
A9 B
(B!
(C!
A9 B9 C9
(&!
A9 C
(C)
Dolution: %6:
A9 B9 C
3eat is supplied to a diatomic gas at constant pressure. Δ / Δ& / Δ> is (!
":%:$
(B!
":$:%
(C!
4:":$
(&!
4:$:"
The ratio of
Ans. (C) %1:
Two mole of argon are mied with one mole of h*drogen2 then C p #C , for the miture is nearl* (!
1.$
(B!
1.%
(C!
1.'
(&!
1."
ns.(C! %$: An %ea 7as s "aken "+7 "e e A → B→C→ A as sn n 47+e. I4 "e ne" ea" s+e% " "e 7as n "e e s 5J9 "e k %ne b "e 7as n "e ess C → A s9
(A) -5J
(B) -10J
(C) -15J Dolution: %%:
(A)
1
(C)
n
γ
(B)
n
()
n
1-
γ
(
>en an %ea #na"# 7as s ea"e% a" ns"an" ess+e9 "e 4a"n 4 ea" ene7 s+e% neases "e n"ena ene7 4 "e 7as s (A)
2'5
(B)
3'5
(C)
3'*
()
3'$
Dolution: %":
A
>en an %ea 7as a" ess+e P9 "e#ea"+e T an% +#e V s s"e#a #esse% " a V'n9 "s ess+e be#es P . I4 "e 7as s #esse% a%aba"a " V'n9 "s ess+e be#es P a. Te a" P ' Pa s
Dolution: %':
() -20J
(B
A #na"# %ea 7as9 n"a a" "e#ea"+e T 1 s ense% n a n%e 4""e% " a 4"ness s"n. Te 7as s ae% " e:an% a%aba"a " a "e#ea"+e T 2 b eeasn7 "e s"n s+%%en. I4 @ 1 an% @2 ae "e en7"s 4 "e 7as +#n be4e an% a4"e e:ansn ese"e9 "en T1'T2 s 7en b (A) (C)
Dolution: %7:
An %ea #n a"# 7as a" 300K e:an%s a%aba"a " "e "s +#e. >a" s "e 4ne "e#ea"+e (A) (C)
Dolution:
%4:
>a" be P-V 7a esn%n7 " "e P-T 7a (ess AB) 4 an %ea 7as sn n 47+e
B
C
P
A
D
T
(A)
Heb
(B)
Ce
(C)
<"a7" ne
()
E"a
Dolution: (A) %8:
<"a"n7 " "e sa#e n"a n%"ns9 an %ea 7as e:an%s 4# +#e V1 " V2 n "ee %44een" as. Te k %ne b "e 7as s >1 4 "e ess s +e s"e#a9 > 2 4 +e sba an% > 3 4 +e a%aba". Ten (A)
>2 = >1 =>3
(B)
>2 = >3 =>1
(C)
>1 = >2 =>3
()
>1 = >3 =>2
(A)
Dolution: %;:
5'2
One #e 4 a7n s ea"e% +sn7 PV ! ns". B a#+n" 4 ea" s b"ane% b "e ess en "e "e#ea"+e an7e b ΔT ! -2K. (A)
100J
(B)
200J
(C)
108J
()
208J
(C)
Dolution: '6:
3 #es 4 an %ea #na"# 7as e4#s a e as sn n "e 47. Te 7as "e#ea"+es T 1 ! $00K9 T 2 ! 800K9 T3 ! 2$00K9 T $ ! 1200K. >a" be "e ne" k %ne.
P
B
A
C
D
T
(A)
20J
(B)
20000J
(C)
200J
()
2000J
'1:
H #+ ea" s absbe% b "e ss"e# n 7n7 "+7 "e ess sn n "e 47. (ns%e "a" a+e s "aken n
100 800
400
V
(A) (C) Dolution: '$:
5
2
3000J 4 ea" s 7en " a 7as a" ns"an" ess+e 4 2 ×10 '# . I4 "s +#e neases b 10 "es %+n7 "e ess9 a" be "e an7e n "e n"ena ene7 4 "e 7as (A)
1000J
(B)
100J
(C)
200J
()
2000J
Dolution: (A) '%: A 7as a" a"#se ess+e s n"ane% n a n%e 4 +#e 80 "e. >en " s #esse% a%aba"a " 20 "e "s ess+e ses " a"#. >a" be "e a" 4 se4 ea"s 4 "e 7as
(A)
1.33
(B)
1.$
(C)
1.*
()
1.5
*
Dolution: (B) '':
A 7as nss"n7 4 7% %a"# #e+es as n"a +n%e s"an%a% n%"ns. Ten 7as as #esse% a%aba"a " ne 44" 4 "s n"a +#e. >a" be "e #ean kne" ene7 4 a "a"n7 #e+e n "e 4na s"a"e? (A)
1.$$ J
(C)
*8*.,8
×
D23
10
(B)
$.55J
()
*5*.3 ×10
-23
J
Dolution: (C) '":
I##e%a"e a4"e "e e:sn 4 an a"# b#b9 "e ba 4 4e %+e% as a a%+s 4 100# an% a "e#ea"+e 105K . >a" be "e a:#a"e "e#ea"+e en "e ba e:an%s a%aba"a " a a%+s 4 1000# (s+se #n a"# 7as s "ee) (A)
1000K
(B)
100K
(C) Dolution: '7:
×
D3 2'3
(10 )
()
200K
(C)
> 4 "e 4n7 s 4ase? (A)
En"a s a a" 4+n"n.
(B)
>k s a a" 4+n"n.
(C)
Hea" s a a" 4+n"n.
()
Ene7 s a s"a"e 4+n"n
Dolution: '4:
105
(C)
A 7as #:"+e nss"s 4 32 7a# 4 :7en an% 3 7a# 4 A a "e#ea"+e T. e7e"n7 ene7 4 "e ss"e# s (A) $RT (C) ,RT
Dolution: '8:
A #n a"# 7as s s+e% ea" e s keen7 "e ess+e ns"an". Te k %ne b "e 7as s (A)
2'5
(B)
3'5
(C)
'5
()
2'3
Dolution: ';:
()
()
> 4 "e 4n7 aa#e"es "e#%na# s"a"e 4 #a""e
%es
n"
aa"ese
(A) (C) Dolution:
"6:
> 4 "e 4n7 s e" (A)
; an s"e#a an7e PV ! ns"an"
(B)
; a s"e#a ess9 "e an7e n n"ena ene7 #+s" be e6+a " "e k %ne γ P 2 - 2 9 ee γ s "e a" 4 "e ; an a%aba" an7e
(C)
=
" se4 ea"s
P1
⎛⎞ ⎜ ⎟ ⎝ V1
"e
In an a%aba" ess e:"ena k %ne #+s" be e6+a ⎠() " "e ea" en"en7 "e ss"e# (A)
Dolution: "1:
An %ea 7as 7es "+7 ess ABC an% 4n7 (P s T) +e s b"ane%. Ts ess an be eesen"e% b
B P C
A
T
B
B P
P C
A
A
C
V
V
(A)
(B)
B B
P P
C
A
V
(C)
C
A
V
()
Dolution:(B) "$:
A n"ane n"an 0.1 # 4 H 2 an% 0.1 # 4 O2 9 I4 "e 7ases ae n "e#a e6+b+# "en (A) On "e aea7e kne" ene7 4 "e #e+e 4 H 2 an% O2 s sa#e. (B)
Aea7e see% 4 "e #e+e 4 H 2 an% O2 s sa#e.
(C) On "e se4 ea" a" ns"an" ess+e 4 " 7ases s sa#e.
() Dolution: "%:
()
T ss"e#s ae n "e#a e6+b+#. Te 6+an"" s ##n 4 "e# s (A)
Hea"
(B)
M#en"+#
(C)
Te#ea"+e
()
<e4 ea"
Dolution: "':
Te se4 ea" a" ns"an" ess+e an% "e kne" ene7 ae sa#e 4 b" "e 7ases.
(C)
Mean #e+a e7" s %e4ne% as (A)
"e n+#be 4 4ee a"es e s"n #ass
(B)
"e n+#be 4 4ee a"es e ee"n #ass
(C)
"e n+#be 4 4ee a"es e ne+"a #ass
()
"e n+#be 4 4ee a"es e "n #ass
Dolution:
()
> ne 4 "e 4n7 s"a"e#en"s s "+e ab+" a 7as "": an a%aba" an7e (A)
Te "e#ea"+e 4 "e 7as e#ans ns"an"
(B)
Te ess+e 4 "e 7as e#ans ns"an"
(C)
Te +#e 4 "e 7as e#ans ns"an"
()
Te 7as s #e"e ns+a"e% 4# "e s++n%n7s
Dolution: "7: "
()
I4 an %ea 7as s ae% " e:an% a%aba"a9 "e k %ne s e6+a (A)
Te ss n ea"
(B)
Te ss n n"ena ene7
(C)
Te 7an n n"ena ene7
()
Te 7an n en"a
Dolution:
"4:
+n%e7n7
(B)
; "e Bes a " %9 "e neessa n%"n s (A)
Is"e#a
(C)
Isba
Dolution: "8:
<e4 ea" 4 a 7as +n%e7n7 a%aba" an7es s (A)
Fe
(B)
n4n"e
(C)
s"e
()
ne7a"e
Dolution: ";:
(B)
Te n"ena ene7 4 "e ss"e# e#ans ns"an" en " +n%e7es (A)
a ess
(B)
an a%aba" ess
(C)
an s"e#a ess
()
an sba ess
Dolution: 76:
(A)
(C)
Te 4s" a 4 "e#%na#s na"es "e ne"s 4 (A)
nsea"n 4 ene7
(B)
nsea"n 4 ea"
(C)
nsea"n 4 k
()
e6+aene 4 ea" an% k
Dolution:
()
