Physics

Thermal Properties and Thermodynamics

431 Questions

Thermal properties and thermodynamics questions evaluate concepts of heat transfer, thermal efficiency, and temperature variations. Problems involve calculating heat content, conductivity, and the performance of heat engines. This subject is regularly tested in physics sections across multiple competitive platforms.

Heat transfer calculationsThermal efficiencyBlack body radiationTemperature variationsRefrigeration performance

Thermal Properties and Thermodynamics Questions

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

Same quantity of ice is filled in each of the two metal containers P and Q having the same size, shape and wall thickness but made of different materials. The containers are kept in identical surroundings. The ice in P melts completely in time $t _1$ whereas that in Q takes a time $t _2$. The ratio of thermal conductivities of the materials of P and Q is

  1. $t _2 : t _1$
  2. $t _1 : t _2$
  3. $t _1^2 : t _2^2$
  4. $t _2^2 : t _1^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The power transported per unit area is given as

$\dfrac{\Delta Q}{A\Delta t}=-\kappa\dfrac{\Delta T}{\Delta x}$
Thus $\Delta Q=-\kappa \Delta tA\dfrac{\Delta T}{\Delta x}$
Same amount of heat was needed to melt ice in both P and Q. Hence 
$\kappa _{P}t _1=\kappa _Qt _2$
$\implies \dfrac{\kappa _P}{\kappa _Q}=\dfrac{t _2}{t _1}$

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

Two plates of same thickness form a composite plate. The temperature on one side of the plate is $0^0 C$. If the ratio of thermal conductivities is 3 : 1 and the plate with higher thermal conductivity has one of its faces at $0^0 C$, then the temperature of the interface is 

  1. $45^0 C$
  2. $40^0 C$
  3. $20^0 C$
  4. $15^0 C$
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

A body P is connected to a large body Q through a conducting rod of length. I crossectional  area. A and thermal conductivity K. This assembly is placed in an an atmosplere of temperature ${ T } _{ A }$ and body Q is also maintained at temperature ${ T } _{ A }$. Let beat capacity of body P is C and it is unitally at temperature ${ T } _{ 1 }$. If in time t second temperature of body P falls to ${ T } _{ 2 }$. Then chose the correct option .

  1. $log\left[ \dfrac { { T } _{ 2 }-{ T } _{ A } }{ { T } _{ 1 }-{ T } _{ A } } \right] =\left[ { K } _{ 1 }\dfrac { KA }{ LC } \right] t$
  2. $log\left[ \dfrac { { T } _{ 2 }-{ T } _{ A } }{ { T } _{ 12 }-{ T } _{ A } } \right] =\left[ { K } _{ 1 }\dfrac { KA }{ LC } \right] t$
  3. $log\left[ \dfrac { { T } _{ 1 }-{ T } _{ A } }{ { T } _{ 2 }-{ T } _{ A } } \right] =\left[ { K } _{ 1 }\dfrac { KA }{ LC } .t \right]$
  4. $log\left[ \dfrac { { T } _{ 1 }-{ T } _{ A } }{ { T } _{ 2 }-{ T } _{ A } } \right] =\left[ { K } _{ 1 }\dfrac { KA }{ LC } \right] t$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The cooling of body P follows Newton's Law of Cooling, where the rate of heat loss dQ/dt = -C(dT/dt) = (kA/L)(T - Ta). Integrating this leads to the natural log form ln((T1 - Ta)/(T2 - Ta)) = (kA/LC)t.

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

A wall has two layers A and B, each made of different material. Both the layers have the same thickness. The thermal conductivity of the material of A is twice that of B. Under thermal equilibrium, the temperature difference across the wall is $36^o$C. The temperature difference across the layer A is?

  1. $6^o$C
  2. $12^o$C
  3. $18^o$C
  4. $24^o$C
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

a wall has two layers $A$ and $B,$ each made of  a different material.Both the layers have the same thickness.The thermal conductivity of the material of $A$ is twice that of $B.$ Under thermal equilibrium, the temperature difference across the wall is ${36^ \circ }C$ The temperature difference across the layer $A$ is  

  1. ${6^ \circ }C$
  2. ${12^ \circ }C$
  3. ${18^ \circ }C$
  4. ${24^ \circ }C$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

An aluminium meter rod of area of cross section $4cm^2$ with K=0.5 cal $g^{-1}$ $^oC^{-1}$ is observed that at steady state 360 cal of heat flows per minute.
The temperature gradient along the rod is

  1. $3^oC/cm$
  2. $6^oC/cm$
  3. $12^oC/cm$
  4. $20^oC/cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Heat flow H = kA(dT/dx). Given H = 360 cal/min = 6 cal/sec, k = 0.5, A = 4. 6 = 0.5 * 4 * (dT/dx). 6 = 2 * (dT/dx), so dT/dx = 3 C/cm.

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

Ratio of radius of curvature of cylindrical emitters of same type is $1:4$ and their temp. are in ration $2:1$. Then ration of amount of heat emitted by them is-(For Cylinder length = radius);-

  1. 2:1

  2. 1:1

  3. 4:1

  4. 1:4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Power radiated P = sigma * A * T^4. For a cylinder, A = 2*pi*r*L + 2*pi*r^2. If L=r, A = 4*pi*r^2. P is proportional to r^2 * T^4. Ratio P1/P2 = (r1/r2)^2 * (T1/T2)^4 = (1/4)^2 * (2/1)^4 = (1/16) * 16 = 1:1.

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

If the coefficient of conductivity of aluminium is $0.5cal/cm-sec-^oC,$ then in order to conduct $10cal/sec-cm^2$ in the steady state, the temperature gradient in aluminium must be

  1. $5^oC/cm$
  2. $10^oC/cm$
  3. $20^oC/cm$
  4. $10.5^oC/cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Heat flux H/A = k * (dT/dx). Given H/A = 10, k = 0.5. 10 = 0.5 * (dT/dx), so dT/dx = 20 C/cm.

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

a rod of length 1 m having cross-sectional area 0.75 $m^{2}$ conduts heat at 6000 $Js^{-1}$. Then the temperature difference across the rod is, if k=200 $Wm^{-1}$ $K^{-1}$

  1. $20^{\circ}C$
  2. $40^{\circ}C$
  3. $80^{\circ}C$
  4. $1000^{\circ}C$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using H = kA(dT/L), 6000 = 200 * 0.75 * (dT/1). 6000 = 150 * dT, so dT = 40 C.

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

A sphere, a cube and a thin circular plate all made of same substance and all have same mass. These are heated to $200^{o}C$ and then placed in a room. Then the:-

  1. Temperature of sphere drops to room temperature at last.

  2. Temperature of cube drops to room temperature at last.

  3. Temperature of thin circular plate drops to room temperature at last.

  4. Temperature of all the three drops to room temperature at the same time
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rate of cooling dT/dt = (sigma * A * e * (T^4 - Ta^4)) / (m * c). For same mass and material, the body with the smallest surface area A cools the slowest. A sphere has the smallest surface area for a given volume/mass, so it takes the longest to cool.

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

A spherical black body of radius $(R)$ when heated to certain temperature and left in vaccum. cools at a rate $'x' $ Now a caity of radius $(R/2)$ is made concentrically from this sphere. The rate of cooling of the remaining sphere will be.....................

  1. $\cfrac { x }{ 8 } $
  2. $\cfrac { 7x }{ 8 } $
  3. $\cfrac { 8x }{ 8 } $
  4. $\cfrac { x }{ 7 } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

A hollow copper sphere and a hollow copper cube, of same surface area and negligible thickness, are filled with warm water of same temperature and placed in an enclosure of constant temperature, a few degrees below that of the bodies. Then in the beginning:

  1. the rate of energy lost by the sphere is greater than that by the cube

  2. the rate of fall of temperature for sphere is greater than that for the cube.

  3. the rate of energy lost by the sphere is less than that by the cube

  4. the rate of fall of temperature for sphere is less than that for the cube.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rate of cooling dT/dt = (sigma * A * (T^4 - Ta^4)) / (m * c). For the same surface area A, the body with the smaller mass m will have a higher rate of temperature fall. A hollow sphere has less volume (and thus less mass) than a hollow cube of the same surface area.

Multiple choice physics temperature and heat modes of heat transfer - conduction conduction heat and modes of heat transfer

A copper block of mass $500gm$ and $Sp.$ Heat $0.1 cal/gm/^{o}{C}$ is heated from ${30}^{o}C$ to ${40}^{o}C$. Another identical copper block $B$ of same mass is heated from ${35}^{o}C$ to ${40}^{o}C$. The ratio of their thermal capacities is 

  1. $1:2$
  2. $2:1$
  3. $1:1$
  4. $1:4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Thermal capacity is defined as mass * specific heat (m * c). Since both blocks have the same mass and are made of the same material (copper), their thermal capacities are identical, resulting in a 1:1 ratio.