Questions and answers for exam Preparation

MCQs

Heat Radiation, Thermal Properties Of Matter, Dual Nature Of Matter

Total Questions : 247 | Page 4 of 25 pages

Question 31. Given that P, V and T stand for vapour pressure, volume and temperature, an ideal gas obeys the law -PV α T. If the volume is kept constant, P α T. With decreasing temperature the vapour pressure drops, until P = 0 at some temperature T₀. Since P cannot be less than zero, or negative, T₀naturally becomes the lowest temperature that we can reach, and can be used as a "natural” lower fixed point while constructing a temperature scale. This is the "absolute zero”, which in the Celsius scale is - 273.15⁰C.

To construct an absolute temperature scale

, where the absolute zero is naturally 0

. Let us choose the triple point of mercury (-38.8⁰C, at 0.2 mPa) as our upper fixed point, and give assign it a value 100

. What will be the boiling point of water on this scale?

121.5
110
159.2
182.7

Discuss Question

Answer: Option C. -> 159.2
:
C
Let the boiling point of water in the near scale be T

. Let's list what we know -

We can, therefore, write -

Question 32. A solid whose volume does not change with temperature floats in a liquid. For two different temperatures

t_{1}

and

t_{2}

of the liquid, fractions

f_{1}

and

f_{2}

of the volume of the solid remain submerged in the liquid. The coefficient of volume expansion of the liquid is equal to

f1−f2f2t1−f1t2
f1−f2f1t1−f2t2
f1+f2f2t1+f1t2
f1+f2f1t1+f2t2

Discuss Question

Answer: Option A. -> f1−f2f2t1−f1t2
:
A
As with the rise in temperature, the liquid undergoes volume expansion therefore the fraction of solid submerged in liquid increases.
Fraction of solid submerged at

{t_{1}}^{\circ} C = f_{1}

= Volume of displaced liquid

= V_{0} (1 + γ t_{1}) \dots \dots (i)

and fraction of solid submerged at

{t_{2}}^{\circ} C = f_{2}

= Volume of displaced liquid

= V_{0} (1 + γ t_{2}) \dots \dots (i i)

From (i) and (ii)

\frac{f_{1}}{f_{2}} = \frac{1 + γ t_{1}}{1 + γ t_{2}}

\Rightarrow

γ = \frac{f_{1} - f_{2}}{f_{2} t_{1} - f_{1} t_{2}}

Question 33. A thermometer is graduated in mm. It registers - 3mm when the bulb of thermometer is in pure melting ice and 22mm when the thermometer is in steam at a pressure of one atm. The temperature in

^{\circ} C

when the thermometer registers 13mm is

1325×100
1625×100
1322×100
1622×100

Discuss Question

Answer: Option B. -> 1625×100
:
B
For a constant volume gas thermometer temperature in

^{\circ} c e n t i g r a d e

is given as

T_{c} = \frac{P - P_{0}}{P_{100} - P_{0}} \times 100^{\circ} C

\Rightarrow

T_{c} = \frac{13 - (- 3)}{22 - (- 3)} \times 100^{\circ} C = \frac{16}{25} \times 100

Question 34. Steam at

100^{o} C

is passed into 1.1 kg of water contained in a calorimeter of water equivalent 0.02 kg at

15^{o} C

till the temperature of the calorimeter and its contents rises to

80^{o} C .

The mass of the steam condensed in kg is
(IIT JEE 1986)

0.130
0.065
0.260
0.135

Discuss Question

Answer: Option D. -> 0.135
:
D
Heat required

Q = (1.1 + 0.02) \times 10^{3} \times 1 \times (80 - 15) = 72800 c a l .

Therefore, mass of steam condensed (in kg)

m = \frac{Q}{L} = \frac{72800}{540} \times 10^{- 3} = 0.135 k g .

Question 35. Two rods of lengths

l_{1}

and

l_{2}

are made of materials whose coefficients of linear expansion are

α_{1}

and

α_{2}

. If the difference between the two lengths is independent of temperature, then

l1l2=α1α2
l1l2=α2α1
l22α1=l21α2
α21l1=α22l2

Discuss Question

Answer: Option B. -> l1l2=α2α1
:
B

L_{1} = l 1 [1 + α_{1} Δ T] L_{2} = l 2 [1 + α_{2} Δ T] L_{1} + L_{2} = (l_{1} + l 2) + (Δ T) (l_{1} α_{1} - l_{2} α_{2}) I f L_{1} - L_{2} i s t o b e i n d e p e n d e n t o f Δ T, t h e n l_{1} α_{1} - l_{2} α_{2} = 0 \Rightarrow \frac{l_{1}}{l 2} = \frac{α_{1}}{α_{2}} \frac{l_{1}}{l 2} = \frac{α_{2}}{α_{1}}

Question 36. On heating a liquid of coefficient of cubical expansion g in a container having coefficient of linear expansion

\frac{g}{3}

, the level of liquid in the container will

Rise
Fall
Will remain almost stationary
It is difficult to say

Discuss Question

Answer: Option C. -> Will remain almost stationary
:
C
Conceptual

Question 37. Steam at

100^{\circ} C

is passed into 1.1 kg of water contained in a calorimeter of water equivalent 0.02 kg at

15^{\circ} C

till the temperature of the calorimeter and its contents rise at

80^{\circ} C

. The mass of the stem condensed in kilogram is

0.130
0.065
0.260
0.135

Discuss Question

Answer: Option A. -> 0.130
:
A
Heat lost by steam = Heat gained by water + calorimeter

∴ m L + m s (100 - 80) = 1.12 \times s \times (80 - 15)

m [540 + (1 \times 20)] = 1.12 \times 1 \times 65

m = \frac{1.12 \times 1 \times 65}{560} = \frac{65}{500} k g o r m = 0.13 k g

Question 38. A block of ice at

- 10^{o} C

is slowly heated and converted to steam at

100^{o} C .

Which of the following curves represents the phenomenon qualitatively?

Discuss Question

Answer: Option A. -> 0.130
:
A

A Block Of Ice At −10oC Is Slowly Heated And Converted To ...

is the correct option. If you don't remember why, you should probably watch the videos on calrimetry again.

Question 39. Browsing through Mr. Fox's old scientific notes, Bruce Wayne encounters a secret temperature scale, which Mr. Fox called Z, in order to keep the Batmobile's technology a secret. On that scale, the freezing and the boiling points of water were recorded to be -7⁰Z and 78⁰Z, respectively. The records instruct to maintain the coolant temperature at -24⁰Z for top speed. Mr. Wayne, naturally comfortable with the Fahrenheit scale due to his American upbringing, needs to calculate the coolant temperature in ⁰F. Help him choose the correct value.

10℉
-4℉
5℉
0

Discuss Question

Answer: Option B. -> -4℉
:
B
Let's list what we know -

Browsing Through Mr. Fox's Old Scientific Notes, Bruce Wayne...

For any general scale with lower and upper fixed points labeled as T_L and T_u, and a measured temperature T, the ratio

will be the same, no matter what scale it is.
Extending that to ⁰Fand ⁰Z(in question), we have -

Question 40. A platinum sphere floats in mercury. Find the percentage change in the fraction of volume of sphere immersed in mercury when the temperature is raised by