1 kJ of heat is given to one mole of an ideal gas and its temperature rises 0 ° C to 100 ° C . If it is kept at a constant pressure throughout the heating, find the change in its internal energy.

In the given question we have to use the concept of internal energy. The change in internal energy will be given by ∆ U = ∆ U f - ∆ U i ⇒ ∆ U = n C v ∆ T - 1000 w h e r e C v = s p e c i f i c h e a t a t c o n s tan t v o l u m e Q = h e a t T = t e m p e r a t u r e n = n o . o f m o l e s ⇒ ∆ U = 1 × 3 2 × 8 . 4 × 100 - 1000 = 1260 - 1000 = 260 J = 0 . 026 K J

One-half mole of helium gas is confined to a container at standard pressure and temperature 1 . 01 × 10 5 Pa , 273 K . How much heat is needed to double the pressure of the gas.

Here, n = 1 2 , C v = 3 J g − 1 K − 1 , M = 4 g m o l − 1 ∴ C v = M C V 4 × 3 = 12 J m o l − 1 K − 1 At constant volume P ∝ T . ∴ P 2 P 1 = T 2 T 1 = 2 , T 2 = 2 T 1 Where C v = specific heat at constant volume P = Pressure T = temperature Rise in temperature Δ T = T 2 − T 1 = 2 T 1 − T 1 = T 1 = 273 K Heat required, Δ Q = N C V Δ T = 21 × 12 × 273 = 1703 . 5 J

A sample of gas is allowed to expand quasistatically and adiabatically, its pressure drops from 120 to 100 Kpa , and its temperature drops from 300 K to 280 K . Is the gas monoatomic or diatomic ?

We know that for adiabatic process, T 1 γ P 1 1 - γ = T 2 γ P 2 1 - γ W h e r e T = t e m p e r a t u r e P = p r e s s u r e ⇒ T 1 γ P 1 1 - γ = T 2 γ P 2 1 - γ ⇒ 300 γ 120 1 - γ = 280 γ 100 1 - γ ⇒ γ = log 1 . 12 1 . 2 ⇒ γ = 2 ⇒ 1 + 2 f = 2 ⇒ f = 2 Hence, the gas is diatomic.

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Specific heat of argon at constant volume is $0.3122 J / kg K$ . Find the specific heat of Argon at constant pressure if $R = 8.314 k J / k m o l e K$ (Molecular weight of argon=39.95) in J/kg K is.

Important Questions on Thermodynamics

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IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 19 - Thermodynamics>EXERCISE>Q 11

The temperature of

20 \times 10^{- 3} kg

of oxygen is raised from

20 ° C

100 ° C

. Calculate the amount of heat absorbed, the increase in internal energy and the amount of work done by the gas when the increase in temperature takes place,
at constant volume.

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IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 19 - Thermodynamics>EXERCISE>Q 11

The temperature of

20 \times 10^{- 3} kg

of oxygen is raised from

20 ° C

100 ° C

. Calculate the amount of heat absorbed, the increase in internal energy and the amount of work done by the gas when the increase in temperature takes place,
at constant pressure. (Given : molar gas constant

R = 8.4 J {mol}^{- 1} K^{- 1}

and

C_{ν}

for oxygen

= 0.155 \times 4200 J {kg}^{- 1} K^{- 1}

)

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 19 - Thermodynamics>EXERCISE>Q 12

An electric heater supplies heat to a system at a rate of 100 W. If the system performs work at a rate of 75 joules per second, at what rate is the internal energy increasing?

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 19 - Thermodynamics>EXERCISE>Q 13

Normal atmospheric pressure is

1.013 \times 10^{5} {Nm}^{- 2}

and the latent heat of melting of ice is

80 cal g^{- 1}

. At

0 ° C

and normal atmospheric pressure the volume of

1 g

of water increases from

1 {cm}^{3}

1.091 {cm}^{3}

on freezing. What will be the change in its internal energy ?

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 19 - Thermodynamics>EXERCISE>Q 14

1 kJ

of heat is given to one mole of an ideal gas and its temperature rises

0 ° C

100 ° C

. If it is kept at a constant pressure throughout the heating, find the change in its internal energy.

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 19 - Thermodynamics>EXERCISE>Q 15

One-half mole of helium gas is confined to a container at standard pressure and temperature

(1.01 \times 10^{5} Pa, 273 K)

. How much heat is needed to double the pressure of the gas.

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 19 - Thermodynamics>EXERCISE>Q 16

A cylinder fitted with a piston contains

0.10 mol

of air at room temperature

(20 ° C)

. The piston is pushed so slowly that the air within the cylinder remains essentially in thermal equilibrium with the surroundings. Find the work done by the air within the cylinder if the final volume is one-half the initial volume.

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IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 19 - Thermodynamics>EXERCISE>Q 17

A sample of gas is allowed to expand quasistatically and adiabatically, its pressure drops from

120

100 Kpa

, and its temperature drops from

300 K

280 K

. Is the gas monoatomic or diatomic ?

Specific heat of argon at constant volume is 0.3122J/kg K. Find the specific heat of Argon at constant pressure if R=8.314 kJ/kmole K (Molecular weight of argon=39.95) in J/kg K is.

Important Questions on Thermodynamics

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Specific heat of argon at constant volume is $0.3122 J / kg K$ . Find the specific heat of Argon at constant pressure if $R = 8.314 k J / k m o l e K$ (Molecular weight of argon=39.95) in J/kg K is.