Title 11. THERMAL PROPERTIES OF MATTER(MOBILE).pdf ✅

SPARK PCMB | DOWNLOAD APP NOW| +91-920-630-6398 11 THERMAL PROPERTIES OF MATTER #QID# 7002 (1.) An amount of water of mass 20 g at 0°C is mixed with 40 g of water 10°C, final temperature of the mixture is (a.) 5°C (b.) 0°C (c.) 20°C (d.) 6.66°C ANSWER: d EXPLANATION: (d) Let θ be the temperature of the mixture. Heat gained by water at 0°C = Heat lost by water at 10°C c m1 (θ − 0) = c m2 (10 − θ) θ = 400 60 = 6.66°C #QID# 7003 (2.) The surface temperature of the stars is determined using (a.) Planck’s law (b.) Wien’s displacement law (c.) Rayleigh-Jeans law (d.) Kirchhoff’s law ANSWER: b EXPLANATION: (b)
SPARK PCMB | DOWNLOAD APP NOW| +91-920-630-6398 The surface temperature of the stars is determined using Wien’s displacement law. According to this (law)λmT = b where b is Wien’s constant whose value is 2.898 × 10−3 mK. #QID# 7004 (3.) Assuming the sun to be a spherical body of radius R at a temperature of T K, evaluate the total radiant power, incident on earth, at a distance r from the sun Where r0 is the radius of the earth and σ is stefan’s constant.v (a.) 4πr0 2R 2σT 4 r 2 ⁄ (b.) πr0 2R 2σT 4 r 2 ⁄ (c.) r0 2R 2σT 4 4πr 2 ⁄ (d.) R 2σT 4 r 2 ⁄ ANSWER: b EXPLANATION: (b) From Stefan’s law, the rate at which energy is radiated by sun at its surface isP = σ × 4πr 2T 4 [Sun is a perfectly black body as it emits radiations of all wavelengths and so for it e=1.] The intensity of this power at earth’s surface(under the assumption r>>r0) is I = P 4πR2 = σ×4πr 2T 4 4πR2 = σR 2σT 4 r 2 The area of earth which receives this energy is only one-half of total surface area of earth, whose projection would be πr0 2 . ∴ Total radiant power as received by earth = πr0 2 × I
SPARK PCMB | DOWNLOAD APP NOW| +91-920-630-6398 = πr0 2×σR 2T 4 r 2 = πr0 2R 2σT 4 r 2 #QID# 7005 (4.) Which one of the following would raise the temperature of 20 g of water at 30°C most when mixed with it? (a.) 20 g of water at 40°C (b.) 40 g of water at 35 °C (c.) 10 g of water at 50°C (d.) 4 g water at 80°C ANSWER: c EXPLANATION: (c) Let m gram of water, whose temperature is θ(> 30°C), be added to 20 g of water at 30°C. If m × 1(θ − θ0 ) = 20 × 1(θ0 − 30) (m+20)θ0 = 60 + mθ θ0 = 600+mθ 20+m For θ0 to be maximum m should be small and θ should be large #QID# 7006 (5.) A cylinder of radius R made of a material of thermal conductivity K1 is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of material of thermal conductivity K2 . The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is (a.) K1 + K2 (b.) K1K2 K1+K2 (c.) K1+3K2 4 (d.) 3K1+K2 4
SPARK PCMB | DOWNLOAD APP NOW| +91-920-630-6398 ANSWER: c EXPLANATION: (c) Both the cylinders are in parallel, for the heat flow from one end as shown Hence Keq = K1A1+K2A2 A1+A2 Where A1 = Area of cross-section of inner cylinder ∝ πR 2 and A2 = Area of cross-section of cylindrical shell = π{(2R) 2 − (R) 2 } = 3πR 2 ⇒ Keq = K1(πR 2 ) + K2(3πR 2 ) πR2 + 3πR2 = K1 + 3K2 4 #QID# 7007 (6.) Which one of the figure gives the temperature dependence of density water correctly? (a.) (b.) (c.) R 2R K2 K1