At 20 ° C , a brass cube has edge length 25 cm . What is the increase in the surface area when it is heated from 20 ° C to 75 ° C ? Take the coefficient of linear expansion of brass as α = 19 × 10 - 6 K - 1

Edge length of brass cube 25 cm , initial temperature = 20 ° C , final temperature = 75 ° C . ∴ Change in temperature is 55 ∘ C . Since, a cube has 6 faces, therefore the surface area is 6 times the area of the square, A = 6 a 2 . Change in area, Δ A = 6 L + Δ L 2 − 6 L 2 ⇒ Δ A = 6 ( ∆ L ) 2 + 12 L Δ L ⇒ Δ A = 12 L Δ L ( Δ L 2 is very small it can be ignored) ( ∵ Δ L = L α Δ T ) ⇒ Δ A = 12 L L α Δ T ⇒ Δ A = 12 α L 2 Δ T ⇒ Δ A = 12 × 19 × 10 − 6 × 25 2 × 10 − 4 × 55 ⇒ Δ A = 7837500 × 10 − 10 ⇒ Δ A = 7 .84 × 10 − 4 m 2 = 7 .84 cm 2 . Increase in surface area when brass cube is heated is 7 . 84 cm 2 .

HARD

JEE Main

IMPORTANT

Earn 100

A $0.485 kg$ sample of liquid water and a sample of ice are placed in a thermally insulated container. The container also contains a device that transfers energy as heat from the liquid water to the ice at a constant rate $P,$ until thermal equilibrium is reached. The temperatures $T$ of the liquid water and the ice are given in the figure below as functions of time $t$ ; the horizontal scale is set by $t_{s} = 80.0 \min .$
(a) What is rate $P ?$
(b) What is the initial mass of the ice in the container?
(c) When thermal equilibrium is reached, what is the mass of the ice produced in this process?

Important Questions on Temperature, Heat, and the First Law of Thermodynamics

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 18 - Temperature, Heat, and the First Law of Thermodynamics>Problems>Q 45

At what temperature is the Fahrenheit scale reading equal to

(a)

three times that of the Celsius scale and

(b)

one-third that of the Celsius scale?

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 18 - Temperature, Heat, and the First Law of Thermodynamics>Problems>Q 46

20 ° C

, a brass cube has edge length

25 cm

. What is the increase in the surface area when it is heated from

20 ° C

75 ° C ?

Take the coefficient of linear expansion of brass as

α = 19 \times 10^{- 6} K^{- 1}

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 18 - Temperature, Heat, and the First Law of Thermodynamics>Problems>Q 47

Given figure represents a closed cycle for gas (the figure is not drawn to scale). The change in the internal energy of the gas as it moves from $a$ to $c$ along the path $a b c$ is $- 50 J$ . As it moves from $c$ to $d, 45 J$ must be transferred to it as heat. An additional transfer of $20 J$ to it as heat is needed as it moves from $d$ to $a$ . How much work is done on the gas as it moves from $c$ to $d$ ?

Question Image

MEDIUM

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 18 - Temperature, Heat, and the First Law of Thermodynamics>Problems>Q 48

20 ° C

, a rod is exactly

20.05 cm

long on a steel ruler. Both are placed in an oven at

250 ° C

, where the rod now measures

20.11

cm

on the same ruler. What is the coefficient of linear expansion for the material of which the rod is made?

MEDIUM

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 18 - Temperature, Heat, and the First Law of Thermodynamics>Problems>Q 49

In the figure (a) two identical rectangular rods of metal are welded end to end, with a temperature of $T_{1} = 0 ° C$ on the left side and a temperature of $T_{2} = 100 ° C$ on the right side. In $6.0 \min, 43 J$ is conducted at a constant rate from the right side to the left side. How much time would be required to conduct $43 J$ if the rods were welded side to side as in Figure (b)?

Question Image

MEDIUM

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 18 - Temperature, Heat, and the First Law of Thermodynamics>Problems>Q 50

An aluminum-alloy rod has a length of

10.000 cm

20.000 ° C

and a length of

10.020 cm

at the boiling point of water. (a) What is the length of the rod at the freezing point of water? (b) What is the temperature if the length of the rod is

10.009 cm

MEDIUM

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 18 - Temperature, Heat, and the First Law of Thermodynamics>Problems>Q 51

In a solar water heater, energy from the sun is gathered by water that circulates through tubes in a rooftop collector. The solar radiation enters the collector through a transparent cover and warms the water in the tubes; this water is pumped into a holding tank. Assume that the efficiency of the overall system is

25 %

(that is,

80 %

of the incident solar energy is lost from the system). What collector area is necessary to raise the temperature of

200 L

of water in the tank from

20 ° C

40 ° C

1.0 h

when the intensity of incident sunlight is

750 W m^{- 2} ?

EASY

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 18 - Temperature, Heat, and the First Law of Thermodynamics>Problems>Q 52

An aluminium flagpole is

30 m

high. By how much does its length increase as the temperature increases by

15 ° C

? [Given

α_{a l u m i n i u m} = 24 \times 10^{- 6} ° C^{- 1}

]

Important Questions on Temperature, Heat, and the First Law of Thermodynamics

Learn and Prepare for any exam you want !