An ice cube of mass 30 g at 0 0 C is left sitting on the kitchen table where it gradually melts and reaches the kitchen temperature of 25 0 C . The latent heat of fusion for ice is 333 J · g - 1 and the specific heat of water is 4 . 2 J · g - 1 · K - 1 . Select the correct statement(s) about this process. (All numerical values in the answers are rounded to the closest integer.)

The entropy of the kitchen does not change

The entropy change of the kitchen is - 48 J · K - 1

The density p versus pressure ( p ) graph of one mole of an ideal monoatomic gas undergoing a cyclic process is shown in the figure. The molecular mass of gas is M . ( a ) Find work done in each process. ( b ) Find heat rejected by gas in one complete cycle. ( c ) Find the efficiency of the cycle.

a For process 1 - 2 , From the graph, it is observed that density ∝ pressure ρ ∝ P ⇒ m v ∝ P ⇒ P V ∝ m ⇒ P V = constant which means it is an isothermal process and the work done is given by, W = n R T ln P 1 P 2 where, n = no of moles R = universal gas constant T = temperature P 1 = pressure at 1 (initial) P 2 = pressure at 2 (final) And from the ideal gas equation, we can write, n R T = P ( V ) = P M P 0 where, M = molecular mass ⇒ W 1 = P M ρ 0 ln P 1 P 2 ⇒ W 1 = P 0 M ρ ln P 0 2 P 0 ⇒ W 1 = P 0 M ρ 0 ln 1 2 ⇒ W 1 = - P 0 M ρ 0 ln 2 and Q 1 = W 1 as △ U 1 = 0 For process 2 - 3 , From the graph, it is observed that the process is isobaric, where pressure remains constant and the work done in this process is W 2 = Q 2 - △ U 2 where Q 2 is heat supplied. △ U 2 is change in internal energy. ( i ) Calculating Q 2 , In isobaric process Q 2 = n C P △ T where, C P = specific heat at constant pressure △ T = change in temperature ⇒ Q 2 = ( 1 ) 5 2 R T 3 - T 2 = 5 2 R T 3 - R T 2 = 5 2 P 3 M ρ 3 - P 2 M ρ 2 = 5 2 2 P 0 M ρ 0 - 2 P 0 M 2 ρ 0 = 2 . 5 P 0 M ρ 0 ii Calculating △ U 2 , In any process △ U 2 = n C V △ T where C V = specific heat at constant volume ⇒ △ U 2 = 1 3 2 R T 3 - T 2 = 3 2 R T 3 - R T 2 = 3 2 P 3 M ρ 3 - P 2 M ρ 2 = 3 2 2 P 0 M ρ 0 - 2 P 0 M 2 ρ 0 = 3 2 P 0 M ρ 0 Now, work done W 2 = Q 2 - △ U 2 W 2 = 2 . 5 P 0 M ρ 0 - 1 . 5 P 0 M ρ 0 W 2 = P 0 M ρ 0 For process 3 - 1 , From the graph, it is observed that density is constant, which means mass volume = constant This implies volume is constant, which is isochoric process. And in this process, work done is zero. W 3 = 0 . b Heat is rejected in ( 1 - 2 ) because Q 1 came out to be negative. Heat is supplied in 2 - 3 because Q 2 came out to be positive. Heat in 3 - 1 process is (isochoric) Q 3 = △ U 3 = n C V △ T = ( 1 ) 3 2 R T 1 - T 3 = 3 2 R T 1 - R T 3 = 3 2 P 0 M ρ 0 - 2 P 0 M ρ 0 = - 3 2 P 0 M ρ 0 Here, also heat is rejected. So, the total heat rejected by gas in one complete cycle is ∑ Q - ve = Q 1 + Q 3 = P 0 M ρ 0 ln 2 + 3 2 P 0 M ρ 0 = P 0 M ρ 0 ln 2 + 3 2 c The efficiency of cycle is given as η = network done heat supplied = W net Q heat is supplied only in 2 - 3 process So, η = W 1 + W 2 + W 3 Q 2 = - P 0 M ρ 0 ln 2 + P 0 M ρ 0 + ( 0 ) 5 2 P 0 M ρ 0 η = 2 5 1 - ln 2

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Earn 100

An ice cube of mass $30 g$ at $0^{0} C$ is left sitting on the kitchen table where it gradually melts and reaches the kitchen temperature of $25^{0} C$ . The latent heat of fusion for ice is $333 J \cdot g^{- 1}$ and the specific heat of water is $4.2 J \cdot g^{- 1} \cdot K^{- 1}$ . Select the correct statement(s) about this process. (All numerical values in the answers are rounded to the closest integer.)

20% studentsanswered this correctly

Important Questions on Thermodynamics

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Second Law of Thermodynamics

Two solid blocks at temperatures

T_{1}

and

T_{2} (T_{1} < T_{2})

are put in thermal contact for a long time inside an insulated container. Choose the correct statement(s).

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Second Law of Thermodynamics

A solid body of constant heat capacity

1 J {(℃)}^{- 1}

is being heated by keeping it in contact with reservoirs in two ways: (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies the same amount of heat. (ii) Sequentially keeping in contact with

8

reservoirs such that each reservoir supplies the same amount of heat. In both, cases the body is brought from initial temperature

100 K

to final temperature

200 K

. Entropy change of the body in the two cases respectively is: Note: This question was awarded as a bonus since temperatures were given in centigrade instead of in Kelvin. Proper corrections are made in the question to avoid it.

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Second Law of Thermodynamics

By leaving the door of a small standard domestic refrigerator open, it is not possible to cool a room, because it violates the ______

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Second Law of Thermodynamics

Consider a two stage Carnot engine. In the first stage heat

Q_{1}

is absorbed at temperature

T

and heat

Q_{2}

is expelled at temperature

α T

(where

α < 1

). In the second stage heat

Q_{2}

is absorbed at temperature

α T

and heat

Q_{3}

is expelled at temperature

β T (β < α) .

The efficiency of the Carnot engine will be

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Second Law of Thermodynamics

A car engine has a power of

20 kW

. The car makes a roundtrip of 1 hour. If the thermal efficiency of the engine is

40 %

and the ambient temperature is

300 K

. The energy generated by fuel combustion is

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Second Law of Thermodynamics

What will be the efficiency of a Carnot engine if it takes heat from reservoir, at

100 ° C

and rejects heat to a sink at,

50 ° C

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Second Law of Thermodynamics

The carnot heat engine have an efficiency of

50 % .

The temperature of sink is maintained at

500 K .

To increase the efficiency upto

80 %,

the increment in the source temperature is

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Second Law of Thermodynamics

Graphs below show the entropy versus energy $U$ of two systems $1$ and $2$ at constant volume. The initial energies of the systems are indicated by $U_{1, i}$ and $U_{2, i},$ respectively. Graphs are drawn to the same scale. The systems are then brought into thermal contact with each other. Assume that, at all times the combined energy of the two systems remains constant. Choose the most appropriate option indicating the energies of the two systems and the total entropy after they achieve the equilibrium.

Question Image

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Second Law of Thermodynamics

One mole of an ideal monatomic gas undergoes the following four reversible processes:
Step

1 :

It is first compressed adiabatically from volume

V_{1}

1 m^{2} .

Step

2 :

then expanded isothermally to volume

10 m^{3}

Step

3 :

then expanded adiabatically to volume

V_{3}

Step

4 :

then compressed isothermally to volume

V_{1} .

If the efficiency of the above cycle is

\frac{3}{4}

then

V_{1}

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Second Law of Thermodynamics

For which of the following processes, entropy change is zero?

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Second Law of Thermodynamics

Entropy of the universe tends to be

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Second Law of Thermodynamics

What is the entropy change in

J K^{- 1}

during the melting of 27.3 g of ice of

0^{o} C

? (Latent heat of fusion of ice = 330

J g^{- 1}

)

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Second Law of Thermodynamics

When water is converted into ice, its entropy

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Second Law of Thermodynamics

Given the following entropy values $(i n J K^{- 1} m o l^{- 1})$ at 298 K and 1 atm : $H_{2} (g) : 130.6, C l_{2} (g) : 223.0, H C l (g) : 186.7.$ The entropy change $(i n J K^{- 1} m o l^{- 1})$ for the reaction

$H_{2} (g) + C l_{2} (g) \overset{}{\to} 2 H C l (g) i s$

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Second Law of Thermodynamics

The density $(p)$ versus pressure $(p)$ graph of one mole of an ideal monoatomic gas undergoing a cyclic process is shown in the figure. The molecular mass of gas is $M$ .

Question Image