Q.1. A cup of coffee cools from 90°C to 80°C in t minutes, when the room temperature is 20°C. The ti me taken by a similar cup of coffee to cool from 80°C to 60°C at room temperature same at 20°C. [2021]
A: 10/13t
B: 5/13t
C: 13/10t
D: 13/5t
Ans: D
According to Newton's law of cooling,
For 1^{st} cup of coffee,
For 2^{nd} cup of coffee,
Divide (1) by (2),
Q.2. The quantities of heat required to raise the temperature of two solid copper spheres of radii r_{1} and r_{2} (r_{1} = 1.5 r_{2}) through 1 K are in the ratio: [2020]
A: 3/2
B: 5/3
C: 27/8
D: 9/4
Ans: C
Q = msΔT s is same as material is same
Q.3. A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is: [2019]
(^{α}C_{u} = 1.7 × 10^{5} K^{1} and α_{Al} = 2.2 × 10^{5} K^{1})
A: 6.8 cm
B: 113.9 cm
C: 88 cm
D: 68 cm
Ans: D
Solution:
α_{Cu}L_{Cu} = α_{Al}L_{Al}
1.7 × 10^{–5} × 88 cm = 2.2 × 10^{5} × L_{Al}
Q.4. The power radiated by a black body is P and it radiates maximum energy at wavelength If the temperature of the black body is now changed so that it radiates maximum energy at wavelength , the power radiated by it becomes nP. The value of n is: [2018]
A: 3/4
B: 4/3
C: 256/81
D: 81/256
Ans: C
Solution:
Q.5. A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be: [2017]
A: 450
B: 1000
C: 1800
D: 225
Ans: C
Solution:
Q.6. Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K_{1} and K_{2}. The thermal conductivity of the composite rod will be: [2017]
A:
B: K_{1} + K_{2}
C: 2(K_{1} + K_{2})
D:
Ans: D
Solution:
Q.7. Coefficient of linear expansion of brass and steel rods are α_{1} and α_{2} . Lengths of brass and steel rods are ℓ_{1} and ℓ_{2} respectively. If (ℓ_{2}  ℓ_{1} ) is maintained same at all temperatures, which one of the following relations holds good ? [2016]
A: α_{1}ℓ_{1} = α_{2}ℓ_{2}
B: α_{1}ℓ_{2} = α_{2}ℓ_{1}
C: α_{1}ℓ_{2}^{2} = α_{2}ℓ_{1}^{2}
D: α_{1}^{2}ℓ_{2} = α_{2}^{2}ℓ_{1}
Ans: A
Solution:
Coefficient of linear expansion of brass = α_{1}
Coefficient of linear expansion = α_{2}
Length of brass and steel rods are l_{1} and l_{2} respectively.
Given,
Increase in length (l_{2}'l_{1}' ) is same for all temperature.
So,
Q.8. A piece of ice falls from a height h so that it melts completely. Only onequarter of the heat produced is absorbed by the ice and all energy of ice gets converted in to heat during its fall. The value of h is : [Latent heat of ice is 3.4 x 10^{5} J/Kg and g = 10 N/kg] [2016]
A: 68 km
B: 34 km
C: 544 km
D: 136 km
Ans: D
Solution:
As per conservation of energy, energy gained by the ice during its fall from height h is given by, E = mgh,
Given, only onequarter of its energy is absorbed by the ice.
So
Q.9. A block body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is U_{1} at wavelength 500 nm is U_{2} and that at 1000 nm is U_{3}. Wien's constant, b = 2.88 x 10^{6} nmK. Which of the following is correct? [2016]
A: U_{1} > U_{2}
B: U_{1} = 0
C: U_{3} = 0
D: U_{2} > U_{1}
Ans: D
Solution:
Given, temperature, T_{1} = 5760 K
Given that energy of radiation emitted by the body at wavelength 250 nm in U_{1}, at wavelength 500 nm is U_{2} and that at 1000 nm is U_{3}.
Now, according to Wein's law, we get
where, b = Wien's constant = 2.88 x 10^{6} nmK
λ_{m} is the wavelength corresponding to maximum energy, so U_{2} > U_{1}.
Given, temperature, T_{1} = 5760 K
Given that energy of radiation emitted by the body at wavelength 250 nm in U1, at wavelength 500 nm is U_{2} and that at 1000 nm is U_{3}.
Now, according to Wein's law, we get
λ_{m}T =b
where, b = Wien's constant = 2.88 x 10^{6} nmK_{ }
_{}
λ_{m} is the wavelength corresponding to maximum energy, so U_{2} > U_{1}.
Q.10. The two ends of a metal rod are maintained at temperatures 100^{o}C and 110^{o}C. the rate of heat flow in the rod is found to be 4.0 J/s. If the ends are maintained at temperatures 200^{o}C and 210^{o}C, the rate of heat flow will be: [2015]
A: 4.0 J/s
B: 44.0 J/s
C: 16.8 J/s
D: 8.0 J/s
Ans: A
Solution:
Here, ΔT_{1} = 110100 = 10^{o} C
As the rate of heat flow is directly proportional to the temperature difference and the temperature difference in both the cases is same i.e. 10^{o} C. So, the same rate of heat will flow in the second case.
Hence,
As the rate of heat flow is directly proportional to the temperature difference and the temperature difference in both the cases is same i.e. 10^{o} C. So, the same rate of heat will flow in the second case.
Hence,
Q.11. On observing light from three different stars P, Q and R, it was found that intensity of violet colour is maximum in the spectrum of P, the intensity of green colour is maximum in the spectrum of R and the intensity of red colour is maximum in the spectrum of Q. If T_{P}, T_{Q} and T_{R} are the respective absolute temperatures of P, Q and R, then it can be concluded from the above observations that: [2015]
A: T_{P} < T_{Q} < T_{R}
B: T_{P} > T_{Q} > T_{R}
C: T_{P} > T_{R} > T_{Q}
D: T_{P} < T_{R} < T_{Q}
Ans: B
Solution:
Q.12. Light with an energy flux of 25 x 10^{4}Wm^{−2} falls on a perfectly reflecting surface at normal incidence. If the surface area is 15 cm^{2}, the average force exerted on the surface is [2014]
A: 1.20 x 10^{−6} N
B: 3.0 x 10^{−6} N
C: 1.25 x 10^{−6} N
D: 2.50 x 10^{−6} N
Ans: D
Solution:
Q.13. Certain quantity of water cools from 70°C to 60°C in the first 5 minutes and to 54° C in the next 5 minutes. The temperature of the surroundings is [2014]
A: 42°C
B: 10°C
C: 45°C
D: 20°C
Ans: C
Solution:
Q.14. Steam at 100°C is passed into 20 g of water at 10°C. When water acquires a temperature of 80°C, the mass of water present will be:
[Take specific heat of water = 1 cal g^{−1} °C^{−1} and latent heat of steam = 540 cal g^{−1}] [2014]
A: 42.5 g
B: 22.5 g
C: 24 g
D: 31.5 g
Ans: B
Solution:
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