Five moles of hydrogen when heated through 20 K expand by an amount of 8 . 3 × 10 - 3 m 3 under a constant pressure of 10 5 N / m 2 . If C v = 20 J mol - 1 K - 1 , find C p .

C v is the amount of heat given to raise the temperature of one mole of hydrogen through 1 K at constant volume. Hence: C v = ∆ Q ∆ T V = ∆ U ∆ T .....(i) This is the heat to increase the internal energy which is the function of temperature only. C p is the amount of heat given to raise the temperature of one mole of hydrogen gas through 1 k at constant pressure. Hence, for one mole of gas: C P = ∆ U ∆ T + P ∆ V ∆ T ......(ii) Using(i) we get: C p = C v + P ∆ V ∆ T ........(iii) Writing the work done for one mole of gas to raise its temperature through 1 K at constant pressure: P ∆ V ∆ T = 8 . 3 × 10 - 3 × 10 5 5 × 20 = 8 . 3 J ......(iv) Using (iii) and (iv) we get: C p = 20 + 8 . 3 × 10 - 3 × 10 5 5 × 20 = 28 . 3 J mol - 1 K - 1

How much steam at 100 ∘ C is to be passed into water of mass 100 g at 20 ∘ C to raise its temperature by 5 ∘ C ? (Latent heat of steam is 540 cal / g and specific heat of water is 1 cal g - 1 C - 1 ∘ )

Let the required mass of steam = M S g Given: Mass of water M W = 100 g Initial temp of the water = 20 ∘ C The final temperature of the water = 25 ∘ C Latent heat of steam L = 540 cal / g Specific heat of the water C = 1 cal g - 1 C - 1 Heat given by steam = Heat taken by water M S × 540 + M S × 1 × 100 - 25 = 100 × 1 × 5 M S = 500 615 = 0 . 813 g Mass of steam required will be 0 . 813 g .

Explain why (a) Two bodies at different temperatures T 1 and T 2 if brought in thermal contact do not necessarily settle to the mean temperature ( T 1 + T 2 )/2.

Till equilibrium is achieved, heat flows from the body at the higher temperature to the body at the lower temperature when two bodies at different temperatures T l and T 2 are brought in thermal contact, i.e., the temperatures of both the bodies become the same. The equilibrium temperature is the same as the mean temperature ( T 1 + T 2 ) 2 only when the thermal capacities of both bodies are equal.

E M B I B E

Intermediate First Year Physics>Chapter 13 - Thermodynamics>EXERCISES>Q 1

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Earn 100

If a monoatomic ideal gas of volume $1 litre$ at N.T.P. is compressed adiabatically to half its volume, find the work done on the gas. $(γ = \frac{5}{3})$

Important Questions on Thermodynamics

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IMPORTANT

Intermediate First Year Physics>Chapter 13 - Thermodynamics>EXERCISES>Q 1

If a monoatomic ideal gas of volume $1 litre$ at N.T.P. is compressed to half of its volume isothermally, find the work done on the gas. $(γ = \frac{5}{3})$

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Intermediate First Year Physics>Chapter 13 - Thermodynamics>EXERCISES>Q 2

Five moles of hydrogen when heated through $20 K$ expand by an amount of $8.3 \times 10^{- 3} m^{3}$ under a constant pressure of $10^{5} N / m^{2}$ . If $C_{v} = 20 J {mol}^{- 1} K^{- 1}$ , find $C_{p}$ .

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IMPORTANT

Intermediate First Year Physics>Chapter 13 - Thermodynamics>EXERCISES>Q 3

How much steam at $100^{\circ} C$ is to be passed into water of mass $100 g$ at $20^{\circ} C$ to raise its temperature by $5^{\circ} C$ ? (Latent heat of steam is $540 cal / g$ and specific heat of water is $1 cal g^{- 1} {}^{\circ}C^{- 1}$ )

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Intermediate First Year Physics>Chapter 13 - Thermodynamics>EXERCISES>Q 13.1

A geyser heats water flowing at the rate of

3.0

litres per minute from

27^{o} C

to

77^{o} C

. If the geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat of combustion is

4.0 \times 10^{4} J / g

?

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Intermediate First Year Physics>Chapter 13 - Thermodynamics>EXERCISES>Q 13.2

What amount of heat must be supplied to $2.0 \times 10^{- 2} kg$ of nitrogen

(at room temperature) to raise its temperature by 45 °C at constant pressure ? (Molecular mass of N₂ = 28; R = 8.3 J mol–1 K–1)

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IMPORTANT

Intermediate First Year Physics>Chapter 13 - Thermodynamics>EXERCISES>Q 13.3

Explain why

(a) Two bodies at different temperatures T₁ and T₂ if brought in thermal contact do
not necessarily settle to the mean temperature (T₁ + T₂ )/2.

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IMPORTANT

Intermediate First Year Physics>Chapter 13 - Thermodynamics>EXERCISES>Q 13.3

Explain why
(b) The coolant in a chemical or a nuclear plant (i.e., the liquid used to prevent the different parts of a plant from getting too hot) should have high specific heat.

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Intermediate First Year Physics>Chapter 13 - Thermodynamics>EXERCISES>Q 13.3

Explain why

(c) Air pressure in a car tyre increases during driving.