JEE Heat Transfer PYQs with Video Solutions, Download PDF

At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm? Both the diameters have been measured at room temperature (27°C).
(Given: coefficient of linear thermal expansion of gold $$\alpha_L = 1.4 \times 10^{-5}$$ K$$^{-1}$$)

A block of ice of mass $$120 \text{ g}$$ at temperature $$0°C$$ is put in $$300 \text{ g}$$ of water at $$25°C$$. The $$x$$ g of ice melts as the temperature of the water reaches $$0°C$$. The value of $$x$$ is ______.
[Use: Specific heat capacity of water $$= 4200 \text{ J kg}^{-1} \text{ K}^{-1}$$, Latent heat of ice $$= 3.5 \times 10^5 \text{ J kg}^{-1}$$]

A lead bullet penetrates into a solid object and melts. Assuming that $$40\%$$ of its kinetic energy is used to heat it, the initial speed of bullet is
(Given, initial temperature of the bullet $$= 127°$$C, Melting point of the bullet $$= 327°$$C, Latent heat of fusion of lead $$= 2.5 \times 10^4$$ J kg$$^{-1}$$, Specific heat capacity of lead $$= 125$$ J kg$$^{-1}$$ K$$^{-1}$$)

A unit scale is to be prepared whose length does not change with temperature and remains $$20 \text{ cm}$$, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is $$40 \text{ cm}$$ and length of iron will be ______ cm.
$$\alpha_{\text{iron}} = 1.2 \times 10^{-5} \text{ K}^{-1}$$ and $$\alpha_{\text{brass}} = 1.8 \times 10^{-5} \text{ K}^{-1}$$.

A hole is drilled in a metal sheet. At 27 °C, the diameter of hole is 5 cm. When the sheet is heated to 177 °C, the change in the diameter of hole is $$d \times 10^{-3}$$ cm. The value of $$d$$ will be _____, if coefficient of linear expansion of the metal is $$1.6 \times 10^{-5} /°C$$

Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of $$8 \times 10^{2}$$ kg m$$^{-3}$$ and specific heat of 2000 J kg$$^{-1}$$K$$^{-1}$$ while the liquid in B has density $$10^{3}$$ kg m$$^{-3}$$ and specific heat of 4000 J kg$$^{-1}$$K$$^{-1}$$. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: When a rod lying freely is heated, no thermal stress is developed in it.
Reason R: On heating, the length of the rod increases.
In the light of the above statements, choose the correct answer from the options given below:

Two identical metal wires of thermal conductivities $$K_1$$ and $$K_2$$ respectively are connected in series. The effective thermal conductivity of the combination is:

Consider a rectangular sheet of solid material of length $$l = 9$$ cm and width $$d = 4$$ cm. The coefficient of linear expansion is $$\alpha = 3.1 \times 10^{-5}$$ K$$^{-1}$$ at room temperature and one atmospheric pressure. The mass of sheet $$m = 0.1$$ kg and the specific heat capacity $$C_v = 900$$ J kg$$^{-1}$$K$$^{-1}$$. If the amount of heat supplied to the material is $$8.1 \times 10^2$$ J then change in area of the rectangular sheet is :

A non-isotropic solid metal cube has coefficients of linear expansion as: $$5 \times 10^{-5}$$/$$^\circ$$C along the x-axis and $$5 \times 10^{-6}$$/$$^\circ$$C along the y and the z-axis. If the coefficient of volume expansion of the solid is $$C \times 10^{-6}$$/$$^\circ$$C then the value of C is

The temperature of a metal strip having coefficient of linear expansion $$\alpha$$ is increased from $$T_1$$ to $$T_2$$ resulting in increase of its length by $$\Delta L_1$$. The temperature is further increased from $$T_2$$ to $$T_3$$ such that the increase in its length is $$\Delta L_2$$. Given $$T_3 + T_1 = 2T_2$$ and $$T_2 - T_1 = \Delta T$$, the value of $$\Delta L_2$$ is ______.

A beaker contains a fluid of density $$\rho$$ $$\frac{kg}{m^3}$$, specific heat $$S$$ $$\frac{J}{kg \cdot ^\circ C}$$ and viscosity $$\eta$$. The beaker is filled up to height h. To estimate the rate of heat transfer per unit area $$\left(\frac{Q}{A}\right)$$ by convection when beaker is put on a hot plate, a student proposes that it should depend on $$\eta$$, $$\left(\frac{S\Delta\theta}{h}\right)$$ and $$\left(\frac{1}{\rho g}\right)$$ when $$\Delta\theta$$ (in $$^\circ C$$) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for $$\left(\frac{Q}{A}\right)$$ is:

One end of a thermally insulated rod is kept at a temperature $$T_1$$ and the other at $$T_2$$. The rod is composed of two sections of lengths $$\ell_1$$ and $$\ell_2$$ and thermal conductivities $$k_1$$ and $$k_2$$ respectively. The temperature at the interface of the two sections is

Ice at $$-20°C$$ is added to 50 g of water at $$40°C$$. When the temperature of the mixture reaches $$0°C$$, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = 4.2 J/g/°C, Specific heat of Ice = 2.1 J/g/°C, Heat of fusion of water at $$0°C$$ = 334 J/g)

Hot water cools from 60°C to 50°C in the first 10 minutes and to 42°C in the next 10 minutes. The temperature of the surroundings is:

A water heater of power 2000 W is used to heat water. The specific heat capacity of water is 4200 J kg$$^{-1}$$ K$$^{-1}$$. The efficiency of heater is 70%. Time required to heat 2 kg of water from 10°C to 60°C is ______ s. (Assume that the specific heat capacity of water remains constant over the temperature range of the water).

Two plates A and B have thermal conductivities $$84$$ W m$$^{-1}$$ K$$^{-1}$$ and $$126$$ W m$$^{-1}$$ K$$^{-1}$$ respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of A and B are kept at $$100°$$C and $$0°$$C respectively, then the temperature of the surface of contact in steady state is _____ °C.

A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $$\theta$$ along the length $$x$$ of the bar from its hot end is best described by which of the following figure.

The specific heat capacity of a substance is temperature dependent and is given by the formula $$C = kT$$, where $$k$$ is a constant of suitable dimensions in SI units, and $$T$$ is the absolute temperature. If the heat required to raise the temperature of 1 kg of the substance from $$-73°$$C to $$27°$$C is $$nk$$, the value of $$n$$ is ______.

[Given: $$0$$ K $$= -273°$$ C.]

200 g water is heated from 40°C to 60°C. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water = 4184 J kg$$^{-1}$$ K$$^{-1}$$):

If the temperature of the sun were to increase from $$T$$ to $$2T$$ and its radius from $$R$$ to $$2R$$, then the ratio of the radiant energy received on earth to what it was previously will be

A liquid in a beaker has temperature $$\theta(t)$$ at time $$t$$ and $$\theta_0$$ is temperature of surroundings, then according to Newton's law of cooling the correct graph between $$\log_e(\theta-\theta_0)$$ and $$t$$ is

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is grams. (Latent heat of fusion of lead $$=2.5\times10^{4}JKg^{-1}$$ and specific heat capacity $$=125JKg^{-1}K^{-1}$$ of lead

A metal ball of mass 0.1 kg is heated upto $$500°C$$ and dropped into a vessel of heat capacity $$800 \text{ JK}^{-1}$$ and containing 0.5 kg water. The initial temperature of water and vessel is $$30°C$$. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, $$4200 \text{ Jkg}^{-1} \text{K}^{-1}$$ and $$400 \text{ Jkg}^{-1} \text{K}^{-1}$$]

In an experiment, a sphere of aluminium of mass 0.20 kg is heated up to 150°C. Immediately, it is put into water of volume 150 cc at 27°C kept in a calorimeter of water equivalent to 0.025 kg. The final temperature of the system is 40°C. The specific heat of the aluminium is (take 4.2 Joule = 1 calorie):

Three conductors of same length having thermal conductivity $$k_1, k_2 \text{ and } K_3$$ are connected as shown in figure.

Area of cross sections of $$ 1^{st} \text{ and }2^{nd}$$ conductor are same and for $$3^{rd}$$ conductor it is double of the $$1^{st}$$ conductor. The temperatures are given in the figure. In steady state condition, the value of 0 is _______ $$^oC$$.
$$(\text{Given }:k_1=60Js^{-1}m^{-1}K^{-1},k_2= 120Js^{-1}m^{-1}K^{-1}, k_3= 135Js^{-1}m^{-1}K^{-1})$$

Two materials having coefficients of thermal conductivity 3K and K and thickness d and 3d respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are $$\theta_2$$ and $$\theta_1$$ respectively, $$(\theta_2 > \theta_1)$$. The temperature at the interface is:

Temperature difference of 120$$^{\circ}$$C is maintained between two ends of a uniform rod $$AB$$ of length $$2L$$. Another bent rod $$PQ$$, of same cross-section as $$AB$$ and length $$\frac{3L}{2}$$, is connected across $$AB$$ (See figure). In steady state, temperature difference between $$P$$ and $$Q$$ will be close to:

A hole is drilled in a metal sheet. At 27 °C, the diameter of hole is 5 cm. When the sheet is heated to 177 °C, the change in the diameter of hole is $$d \times 10^{-3}$$ cm. The value of $$d$$ will be _____$$10^{-3} cm$$, if coefficient of linear expansion of the metal is $$1.6 \times 10^{-5}$$ / °C

An experiment takes 10 min to raise the temperature of water in a container from 0$$^\circ$$C to 100$$^\circ$$C and another 55 min to convert it totally into steam by a heater supplying heat at a uniform rate. Neglecting the specific heat of the container and taking specific heat of the water to be 1 cal (g$$^\circ$$C)$$^{-1}$$, the heat of vaporization according to this experiment will come out to be:

1 kg of water, at 20°C is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of 20 Ω. The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time taken for water to evaporate fully is close to
[Specific heat of water = 4200 J kg$$^{-1}$$ °C$$^{-1}$$ Latent heat of water = 2260 kJ kg$$^{-1}$$]