Specific Heat Capacity and Latent Heat

Specific Heat Capacity and Latent Heat

Which of the following correctly describes the First Law of Thermodynamics?

**Specific heat capacity** c = Q/(m ΔT) (J/kg·K), molar C = Q/(n ΔT), heat required to raise temperature, Q = m c ΔT, for water c=4186 J/kg·K, latent heat L = Q/m for phase change at constant temperature, fusion L_f and vaporization L_v, Q = m L, e.g., ice melting L_f=3.34×10⁵ J/kg, water vaporization 2.26×10⁶ J/kg. The First Law ( Δ Q = Δ U + Δ W ) states that heat added equals the increase in internal energy plus work done by the system, a form of energy conservation. Option B is correct. Using first law ΔU = Q - W, W = ∫

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Specific Heat Capacity and Latent Heat

In an isobaric process, 0.6 moles of gas expand from 400 K to 480 K . What is the heat supplied if C_p = 25.0 J mol⁻¹ K⁻

**Latent heat** energy needed for phase change without temperature change, overcomes intermolecular forces, e.g., heating ice at 0°C to water at 0°C requires 334 kJ/kg, then heating water to 100°C requires c ΔT, then vaporization 2260 kJ/kg, illustrating two types of heat. Δ Q = μ C_p Δ T . μ = 0.6 , C_p = 25.0 , Δ T = 480 - 400 = 80 . Δ Q = 0.6 × 25.0 × 80 = 1200 J . Using first law ΔU = Q - W, W = ∫ P dV, isobaric W = P ΔV, isothermal W = n R T ln(V₂/V₁), adiabatic

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Specific Heat Capacity and Latent Heat

A gas undergoes an adiabatic compression from 18 L to 6 L , increasing its pressure from 4 atm to 12 atm . What is the v

**Heat capacity** at constant pressure C_p and volume C_v, C_p = C_v + R per mole, for solids Dulong-Petit C_v≈3R≈25 J/mol·K. Specific heat and latent heat govern temperature changes and phase transitions, Q = m c ΔT for heating, Q = m L for melting/boiling at constant T. For adiabatic: P₁ V₁^γ = P₂ V₂^γ . 4 × 18^γ = 12 × 6^γ . (18^γ)/(6^γ) = (12)/(4) ⇒ ((18)/(6))^γ = 3 ⇒ 3^γ = 3¹ . γ = 1 , but check context—PDF uses γ > 1 , approximate γ = 1.33 from typical values.Correction: 3^γ = 3 , but recheck: 18¹.33 / 6¹.33 ≈

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Specific Heat Capacity and Latent Heat

In a thermodynamic process, what indicates that a variable is not in equilibrium?

**Specific heat capacity** c = Q/(m ΔT) (J/kg·K), molar C = Q/(n ΔT), heat required to raise temperature, Q = m c ΔT, for water c=4186 J/kg·K, latent heat L = Q/m for phase change at constant temperature, fusion L_f and vaporization L_v, Q = m L, e.g., ice melting L_f=3.34×10⁵ J/kg, water vaporization 2.26×10⁶ J/kg. A system not in equilibrium has macroscopic variables (e.g., pressure, temperature) that change with time or vary across the system, such as during rapid expansion or explosive reactions, where uniformity is lost. Using first law ΔU = Q - W, W = ∫ P dV, isobaric W = P

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Specific Heat Capacity and Latent Heat

Which of the following statements is incorrect about work in thermodynamics?

**Latent heat** energy needed for phase change without temperature change, overcomes intermolecular forces, e.g., heating ice at 0°C to water at 0°C requires 334 kJ/kg, then heating water to 100°C requires c ΔT, then vaporization 2260 kJ/kg, illustrating two types of heat. Work ( W = P Δ V ) is path-dependent, not a state variable, and involves mechanical energy transfer, not temperature differences (unlike heat). Option C is incorrect. Using first law ΔU = Q - W, W = ∫ P dV, isobaric W = P ΔV, isothermal W = n R T ln(V₂/V₁), adiabatic P V^γ = const and η = 1 -

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Specific Heat Capacity and Latent Heat

How much heat is required to raise the temperature of 0.4 kg of tungsten from 40^circ C to 70^circ C ? (Specific heat of

**Heat capacity** at constant pressure C_p and volume C_v, C_p = C_v + R per mole, for solids Dulong-Petit C_v≈3R≈25 J/mol·K. Specific heat and latent heat govern temperature changes and phase transitions, Q = m c ΔT for heating, Q = m L for melting/boiling at constant T. Δ Q = m s Δ T . m = 0.4 , s = 134.4 , Δ T = 70 - 40 = 30 . Δ Q = 0.4 × 134.4 × 30 = 1612.8 J ≈ 1613 J . Using first law ΔU = Q - W, W = ∫ P dV, isobaric W = P

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Specific Heat Capacity and Latent Heat

A gas expands adiabatically from 8 atm and 16 L to 2 atm . What is the final volume? ( gamma = 1.5 )

**Specific heat capacity** c = Q/(m ΔT) (J/kg·K), molar C = Q/(n ΔT), heat required to raise temperature, Q = m c ΔT, for water c=4186 J/kg·K, latent heat L = Q/m for phase change at constant temperature, fusion L_f and vaporization L_v, Q = m L, e.g., ice melting L_f=3.34×10⁵ J/kg, water vaporization 2.26×10⁶ J/kg. P₁ V₁^γ = P₂ V₂^γ . 8 × 16¹.5 = 2 × V₂¹.5 . V₂¹.5 = (8)/(2) × 16¹.5 = 4 × 16¹.5 . 16¹.5 = 16 × 16⁰.5 = 64 , V₂¹.5 = 4 × 64 = 256 . V₂ = 256¹/1.5 = 256²/3 ≈ 40.3 L .

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Specific Heat Capacity and Latent Heat

In an isobaric process, 1.5 moles of an ideal gas expand from 5 L to 15 L at 300 K . What is the work done by the gas? (

**Latent heat** energy needed for phase change without temperature change, overcomes intermolecular forces, e.g., heating ice at 0°C to water at 0°C requires 334 kJ/kg, then heating water to 100°C requires c ΔT, then vaporization 2260 kJ/kg, illustrating two types of heat. W = P Δ V , P V = μ R T .Initial P = (μ R T)/(V₁) = (1.5 × 8.3 × 300)/(5) = 747 atm (unit adjustment needed).Correctly: W = μ R T ((V₂ - V₁)/(V₁)) , but simply W = P Δ V . Δ V = 15 - 5 = 10 L , adjust units: W = μ R

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Specific Heat Capacity and Latent Heat

What is the significance of the P-V relationship in an adiabatic process for an ideal gas?

**Heat capacity** at constant pressure C_p and volume C_v, C_p = C_v + R per mole, for solids Dulong-Petit C_v≈3R≈25 J/mol·K. Specific heat and latent heat govern temperature changes and phase transitions, Q = m c ΔT for heating, Q = m L for melting/boiling at constant T. In an adiabatic process, P V^γ = constant (where γ = (C_p)/(C_v) ) reflects the trade-off between pressure and volume without heat exchange, linking work done to internal energy changes. Using first law ΔU = Q - W, W = ∫ P dV, isobaric W = P ΔV, isothermal W = n R T ln(V₂/V₁), adiabatic P

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Specific Heat Capacity and Latent Heat

Why does the specific heat capacity of a gas differ at constant pressure and constant volume?

**Specific heat capacity** c = Q/(m ΔT) (J/kg·K), molar C = Q/(n ΔT), heat required to raise temperature, Q = m c ΔT, for water c=4186 J/kg·K, latent heat L = Q/m for phase change at constant temperature, fusion L_f and vaporization L_v, Q = m L, e.g., ice melting L_f=3.34×10⁵ J/kg, water vaporization 2.26×10⁶ J/kg. At constant pressure ( C_p ), heat supplies energy for both internal energy increase and work done due to expansion ( Δ Q = Δ U + P Δ V ). At constant volume ( C_v ), no work is done ( Δ V = 0 ), so heat

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Specific Heat Capacity and Latent Heat

In an adiabatic process, a gas expands from a volume of 1 L to 4 L , reducing its pressure from 16 atm to 1 atm . What i

**Latent heat** energy needed for phase change without temperature change, overcomes intermolecular forces, e.g., heating ice at 0°C to water at 0°C requires 334 kJ/kg, then heating water to 100°C requires c ΔT, then vaporization 2260 kJ/kg, illustrating two types of heat. For an adiabatic process, P₁ V₁^γ = P₂ V₂^γ .Substitute: 16 × 1^γ = 1 × 4^γ . 16 = 4^γ .Taking log: log(16) = γ log(4) . log(16) = log(2⁴) = 4 log(2) , log(4) = log(2²) = 2 log(2) . 4 log(2) = γ × 2 log(2) ⇒ γ = (4)/(2) = 2 . Using first law ΔU = Q -

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Specific Heat Capacity and Latent Heat

A system releases 600 J of heat and performs 250 J of work. What is the change in internal energy?

**Heat capacity** at constant pressure C_p and volume C_v, C_p = C_v + R per mole, for solids Dulong-Petit C_v≈3R≈25 J/mol·K. Specific heat and latent heat govern temperature changes and phase transitions, Q = m c ΔT for heating, Q = m L for melting/boiling at constant T. First Law: Δ Q = Δ U + Δ W . Δ Q = -600 J (heat released), Δ W = 250 J (work by system). -600 = Δ U + 250 ⇒ Δ U = -600 - 250 = -850 J . Using first law ΔU = Q - W, W = ∫ P dV, isobaric

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