A gas in a cylinder is held at a constant pressure of 2 . 30 × 10 5 Pa and is cooled and compressed from 1 . 70 m 3 to 1 . 20 m 3 . The internal energy of the gas decreases by 1 . 40 × 10 5 J . ( a ) Find the work done by the gas. ( b ) Find the absolute value | Q | of the heat flow into or out of the gas and state the direction of the heat flow. ( c ) Does it matter whether, or not, the gas is ideal? Why or why not?

Solution for ( a ) : Given: A gas is cooled and compressed at constant pressure, P = 2 . 30 × 10 5 Pa , from volume 1 . 70 m 3 to 1 . 20 m 3 . So, for a change in volume of ∆ V , the work done is W = p ∆ V ⇒ W = 2 . 30 × 10 5 Pa 1 . 20 - 1 . 70 m 3 ⇒ W = - 1 . 15 × 10 5 J Solution for ( b ) : Given: The decrease in internal energy of the gas, ∆ U = - 1 . 40 × 10 5 J According to the first law of thermodynamics, the heat absorbed by the system from the surrounding is, Q = ∆ U + W ⇒ Q = - 1 . 40 × 10 5 J + - 1 . 15 × 10 5 J ∴ Q = - 2 . 55 × 10 5 J Therefore, the net heat rejected by the system is Q = 2 . 55 × 10 5 J . Solution for ( c ) : It does not matter whether the gas is ideal or not, because first Law of thermodynamics can be applied for an ideal and as well as a non-ideal substance.

When a gas expands along A B , it does 500 J of work and absorbs 250 J of heat. When the gas expands along A C , it does 700 J of work and absorbs 300 J of heat. ( a ) How much heat does the gas exchange along B C ? ( b ) When the gas makes a transition from C to A along C D A , 800 J of work is done on it from C to D . How much heat does it exchange along C D A ?

Solution for ( a ) : Work done by the gas along A B , W AB = 500 J Heat absorbed by the gas along A B , Q AB = 250 J Work done by the gas along A C , W AC = 700 J Heat absorbed by the gas along A C , Q AC = 300 J From the first law of thermodynamics, Q = ∆ U + W Along A C , Q AC = U C - U A + W AC ⇒ U C - U A = Q AC - W AC ⇒ U C - U A = 300 J - 700 J ⇒ U C - U A = - 400 J . . . 1 Along A B , Q AB = U B - U A + W AB ⇒ U B - U A = Q AB - W AB ⇒ U B - U A = 250 J - 500 J ⇒ U B - U A = - 250 J . . . 2 From the given P - V graph, since volume of the gas remains same along B C , work done along B C , W BC = 0 . By subtracting equations 1 and 2 , we get, U C - U A - U B - U A = - 400 J - - 250 J ⇒ U C - U B = - 150 J From the first law of thermodynamics, along B C , Q BC = U C - U B + W BC ⇒ Q BC = - 150 J + 0 ∴ Q BC = - 150 J . Solution for ( b ) : Given: Work done on the gas in the process C → D , W CD = - 800 J , From the given P - V graph, since volume of the gas remains same along D A , work done along D A , W DA = 0 From the first law of thermodynamics, along C D A , Q CDA = U A - U C + W CD + W DA ⇒ Q CDA = 400 J + - 800 J + 0 ∴ Q CDA = - 400 J

A 1 . 0 kg bar of copper is heated at atmospheric pressure 1 . 01 × 10 5 N m - 2 . If its temperature increases from 20 ° C to 50 ° C , calculate the change in its internal energy. α = 7 . 0 × 10 - 6 ° C - 1 , ρ = 8 . 92 × 10 3 kg m - 3 and c = 387 J kg - 1 ° C - 1

Given: Mass of copper bar, m = 1 . 0 kg Coefficient of linear expansion, α = 7 . 0 × 10 - 6 ° C - 1 Density of the bar, ρ = 8 . 92 × 10 3 kg m - 3 Specific heat capacity, c = 387 J kg - 1 ° C - 1 Pressure, P = 1 . 01 × 10 5 N m - 2 Volume of the bar, V = m ρ = 1 8 . 92 × 10 3 ⇒ V = 1 . 12 × 10 - 4 m 3 We know, change in volume ∆ V = V γ ∆ T , where γ is the coefficient of volumetric expansion, ⇒ γ = 3 α . So, ∆ V = 1 . 12 × 10 - 4 3 7 . 0 × 10 - 6 30 ⇒ ∆ V = 7 . 056 × 10 - 8 m 3 Now, work done, W = P ∆ V ⇒ W = 1 . 01 × 10 5 7 . 056 × 10 - 8 ⇒ W = 7 . 126 × 10 - 3 J Heat supplied to the copper bar, Q = m c ∆ T ⇒ Q = 1 387 30 ∴ Q = 11610 J

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Five moles of an ideal monoatomic gas with an initial temperature of $127 ° C$ expand and in the process absorbs $1200 J$ of heat and do $2100 J$ of work. What is the final temperature of the gas?

Important Questions on Laws of Thermodynamics

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JEE Advanced

IMPORTANT

Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 5 - Laws of Thermodynamics>Exercises>Q 11

Find the change in internal energy of $2 kg$ of water as it is heated from $0 ° C$ to $4 ° C$ . The specific heat capacity of water is $4200 J {kg}^{- 1} K^{- 1}$ and its densities at $0 ° C$ and $4 ° C$ are $999 .9 kg m^{- 3}$ and $1000 kg m^{- 3}$ , respectively. (Atmospheric pressure $= 10^{5} Pa$ .)

HARD

JEE Advanced

IMPORTANT

Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 5 - Laws of Thermodynamics>Exercises>Q 12

Calculate the increase in the internal energy of $10 g$ of water when it is heated from $0 ° C$ to $100 ° C$ and converted into steam at $100 kPa$ .

The density of steam $= 0.6 kg m^{- 3}$ , specific heat capacity of water $= 4200 J {kg}^{- 1} ° C^{- 1}$ and the latent heat of vaporization of water $= 2.5 \times 10^{6} J {kg}^{- 1}$ .

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JEE Advanced

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Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 5 - Laws of Thermodynamics>Exercises>Q 14

A gas in a cylinder is held at a constant pressure of

2.30 \times 10^{5} Pa

and is cooled and compressed from

1.70 m^{3}

1.20 m^{3}

. The internal energy of the gas decreases by

1.40 \times 10^{5} J

(a)

Find the work done by the gas.

(b)

Find the absolute value

| Q |

of the heat flow into or out of the gas and state the direction of the heat flow.

(c)

Does it matter whether, or not, the gas is ideal? Why or why not?

HARD

JEE Advanced

IMPORTANT

Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 5 - Laws of Thermodynamics>Exercises>Q 15

$P - V$ diagram of an ideal gas for a process $A B C$ is as shown in the figure.

Question Image

$(a)$ Find the change in internal energy of the gas during the process $A B C$ .
$(b)$ Find total heat absorbed or released by the gas during the process $A B C$ .
$(c)$ Plot pressure versus density graph of the gas for the process $A B C$ .

HARD

JEE Advanced

IMPORTANT

Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 5 - Laws of Thermodynamics>Exercises>Q 16

In the given graph, an ideal gas changes its state from $A$ to $C$ by two paths $A B C$ and $A C$ .

Question Image .

$(a)$ Find the path along which work done is less.
$(b)$ The internal energy of gas at $A$ is $10 J$ and the amount of heat supplied in path $A C$ is $200 J$ . Calculate the internal energy of the gas at $C$ .
$(c)$ The internal energy of gas at state $B$ is $20 J$ . Find the amount of heat supplied to the gas to go from $A$ to $B$ .

HARD

JEE Advanced

IMPORTANT

Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 5 - Laws of Thermodynamics>Exercises>Q 17

When a gas expands along $A B$ , it does $500 J$ of work and absorbs $250 J$ of heat. When the gas expands along $A C$ , it does $700 J$ of work and absorbs $300 J$ of heat.

Question Image

$(a)$ How much heat does the gas exchange along $B C$ ?
$(b)$ When the gas makes a transition from $C$ to $A$ along $C D A$ , $800 J$ of work is done on it from $C$ to $D$ . How much heat does it exchange along $C D A$ ?

HARD

JEE Advanced

IMPORTANT

Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 5 - Laws of Thermodynamics>Exercises>Q 18

1.0 kg

bar of copper is heated at atmospheric pressure

(1.01 \times 10^{5} N m^{- 2})

. If its temperature increases from

20 ° C

50 ° C

, calculate the change in its internal energy.

α = 7.0 \times 10^{- 6} ° C^{- 1}

ρ = 8.92 \times 10^{3} kg m^{- 3}

and

c = 387 J {kg}^{- 1} ° C^{- 1}

HARD

JEE Advanced

IMPORTANT

Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 5 - Laws of Thermodynamics>Exercises>Q 19

One mole of an ideal monoatomic gas occupies a volume of

1.0 \times 10^{- 2} m^{3}

at a pressure of

2.0 \times 10^{5} N m^{- 2}

(a)

What is the temperature of the gas?

(b)

The gas undergoes an adiabatic compression until its volume is decreased to

5.0 \times 10^{- 3} m^{3}

. What is the new gas temperature?

(c)

How much work is done on the gas during the compression?

(d)

What is the change in the internal energy of the gas?

Five moles of an ideal monoatomic gas with an initial temperature of 127°C expand and in the process absorbs 1200 J of heat and do 2100 J of work. What is the final temperature of the gas?

Important Questions on Laws of Thermodynamics

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Five moles of an ideal monoatomic gas with an initial temperature of $127 ° C$ expand and in the process absorbs $1200 J$ of heat and do $2100 J$ of work. What is the final temperature of the gas?