Maharashtra State Board
- A gas in a closed container is heated with 10J of energy, causing the lid of the container to rise 2m with 3N of force (B) 4J the total change in energy of the system is 4J 2
- Find the temperature of a blackbody if its spectrum has a peak at (a) λmax = 700 nm = 700×10^(-9 )m, (b) λmax = 3 cm = 3×10^(-2 )m, (c) λmax = 3 m b = 2.897 × 10⁻³ m K (a) T= b/λmax = (2.897 × 10⁻³ )/ (700×... 1
- A small-blackened solid copper sphere of radius 2.5 cm is placed in an evacuated chamber. Given : r = 2.5 cm = 2.5 ×10⁻²m, T₀ = 273+100 = 373 K, T = 273+110 = 383 K, σ = 5.76 × 10⁻⁸ J s⁻¹ m⁻² K⁻⁴ The rate at which energy must be s... 2
- Earth’s mean temperature can be assumed to be 280 K. Given: T = 280 K, Wien's constant b = 2.897×10⁻³ m.K λ_maxT = b λ_max = b /T = 2.897×10⁻³ / 280 = 1.035 ×10⁻⁵ m This value lies in the infra... 1
- Compare the rates of emission of heat by a blackbody maintained at 727 ºC and at 227ºC Given: T₁ = 273 + 727 = 1000 K, T₂ = 273 + 227 = 500 K, T₀ = 273 + 27 = 300 K i) The rate of emission of heat, dQ/dt = σAT⁴ we assume that t... 1
- The emissive power of a sphere of area 0.02 m2 is 0.5 kcal s-1 m-2. What is the amount of heat radiated Given : R = 0.5 kcal-s⁻¹ 'm⁻² , A =0.02 m², t=20s Q = RAt = (0.5) (0.02) (20) = 0.2 kcal 0.2 kcal is the required quantity. 1
- Energy is emitted from a hole in an electric furnace at the rate of 20 W, when the temperature of the furnace is 727 ºC. Given: Q/t = 20W, T=273+727=1000 K, σ = 5.7×10⁻⁸ Js⁻¹/m².K⁻⁴ Q/t = σAT⁴ ∴ The area of the hole, A = (Q/t)/(σT⁴ ) = 20(5.7×10⁻⁸ ×1000⁴ ) = 20... 1
- Calculate the energy radiated in one minute by a blackbody of surface area 100 cm2 when it is maintained at 227 ºC. Given: t = one minute = 60 s, A = 100 cm² = 100×10⁻⁴ m² = 10⁻² m², T = 273 + 227 = 500 K, σ= 5.67×10⁻⁸ W/m².K⁴ The energy radiated, Q = σAT⁴... 1
- Calculate the average molecular kinetic energy (i) per kmol (ii) per kg (iii) per molecule of oxygen at 127 ºC Given : T = 273+127 = 400 K, molecular weight=32 \ molar mass = 32 kg/kmol, R = 8.31 Jmol⁻¹ K⁻¹, N_A = 6.02 x 10²³ molecules mol⁻¹ (i) The a... 1
- Find kinetic energy of 5 litre of a gas at S.T.P. given standard pressure is 1.013 × 105 N/m2 Given : P 1.013 x 10⁵ N/m², V = 5 litres = 5 x 10⁻³ m E = 3/2 PV = 3/2 (1.013 x 10⁵) (5 x 10⁻³) = 7.5 x 1.013 x 10² J = 7.597 x 10² J This i... 1
- Compare the rms speed of hydrogen molecules at 127 ºC with rms speed of oxygen molecules at 27 ºC M_(o1 )(hydrogen) = 2 g/mole M_(o2 )(oxygen) = 32 g/mole T_(1 )(hydrogen) = 273+127=400 K T_(2 )(oxygen) = 273+27=300 K The rms speed v_rms... 1
- At what temperature will oxygen molecules have same rms speed as helium molecules at S.T.P.? Given : T_(2 )= 273 k, M_o1 (oxygen)= 32 ×10^(-3 )kg/mole, M_o2 (hydrogen)= 4 ×10^(-3 )kg/mole v_rms = √(3RT/M_o) The rms speed of oxygen mo... 1
- Show that rms velocity of an oxygen molecule is 2 times that of a sulfur dioxide molecule at S.T.P. Given : m_o(SO₂)/m_o(O₂) = 64/32 =2 The rms speed v_rms = √(3RT/M_o) v_rms ∝ 1/√(M_o) at constant T fracv_rms(O₂)v_rms(SO₂) = √(M_o(SO₂)/M_o... 1
- A gas in a cylinder is at pressure P. If the masses of all the molecules are made one third of their original Given: m_(2 )= m₁/3 v_(2 )= 2v₁ Pressure P= 1/3 mN/vv² ∴P₁= 1/3 m₁N/vv₁² ∴P₂= 1/3 m₂N/vv₂² ∴ P₁/P₂ =(m₂/m₁)(v₂²/v₁²) = m₁/3/m₁(2²) = 4/3 P₂... 1
- Two vessels A and B are filled with same gas where volume Given : V_(A )= V_(B ), T_A=2T_(B )P_A=2P_B PV=Nk_BT ∴ No of molecules, N=PV/k_BT N_A=P_AV_A/k_BT_(A )and N_B=P_BV_B/k_BT_B ∴ N_A/N_(B )= (P... 1
- Calculate the ratio of mean square speeds of molecules of a gas at 30 K and 120 K. Given : T₁ = 30K, T₂= 120K The mean square speed v² = 3RT/M_o ∴ v₁²/v₂² =T₁/T₂ for given gas ∴ v₁²/v₂² =30K/120K = 1/4 1/4 is the ratio 1
- State and prove Kirchoff’s law of heat radiation. Kirchhoff’s law of heat radiation: At a given temperature, the ratio of the emissive power to the coefficient of absorption of a body is equ... 1
- Explain spectral distribution of blackbody radiation. Answer: the spectral distribution of blackbody radiation is the graph of energy emitted per unit wavelength ( E_λ ) against wavelength ( λ )... 1
- state Wein’s displacement law. Wien’s displacement law : The wavelength for which the emissive power of a blackbody is maximum, is inversely proportional to the absolute t... 1
- state Stefan-Boltmann law The Stefan-Boltzmann law : The rate of emission of radiant energy per unit area or the power radiated per unit area of a perfect blackbody i... 1
- State the law of equipartition of energy and hence calculate molar specific heat of mono- and di-atomic gases Law of equipartition of energy states that for a dynamical system in thermal equilibrium the total energy of the system is shared equally by... 1
- Mention the conditions under which a real gas obeys ideal gas equation. A real gas obeys ideal gas equation when temperature is very high and pressure is very low. 1
- Explain, on the basis of kinetic theory, how the pressure of gas changes if its volume is reduced at constant temperatur The average kinetic energy per molecule of a gas is constant at constant temperature. When the volume of a gas is reduced at constant temper... 1
- When a gas is heated its temperature increases. Explain this phenomenon based on kinetic theory of gases. Molecules of a gas are in a state of continuous random motion. They possess kinetic energy. When a gas is heated, there is increase in the a... 1